Here is my take. There 3 types of options:

Web based services that fully implement and enforce rules for their games

• Boardgamearena - the best selection in this category by far. These days games are added much faster than normal players will be able to keep up with so there is always plenty to explore. Very large player base, for popular games you will find matches quickly. Good match-making and lots of play modes: real-time, turn-based (with customizable time allowances), Arena, Tournaments. Generally high quality implementations that tend to stay visually true to the physical version of the game. Many games have good tutorials. The premium subscription is not strictly required but an excellent value if you use the site a lot. BGA has been invaluable in my boardgame journey. It has allowed me to learn and try hundreds of games and I must have bought at least 50 physical games based primarily on my BGA experience. Too many favorites to list.

• Yucata.de - moves slower but over the years it has built up a decent repertoire and it has some real gems that you won't find elsewhere. Primarily for turn-based play (unless you find a group of people who commits to quick turns). The UI is a bit quirky but after getting used to it I like a lot of things about it. In my opinion Yucata has the best undo and replay/review implementation out there. My favorites here are Grand Austria Hotel, Newton, Mottainai, Taverns of Tiefenthal, Lorenzo Il Magnifico. Rajas of the Ganges (and Rajas Dice), Targi, Fields of Arle. Yucata has "sold" me a bunch of games too.

• triqqy.com, happymeeple.com, brettspielwelt.de, rally-the-troops.com, boiteajeux.net, warchestonline.com are some other sites that I visit for specific games. These have smaller player bases but worth checking out to see if they have one of your favorites.

Virtual tabletops that don't enforce the rules

• Tabletop Simulator is a desktop app that's available for purchase on Steam. As the name suggests this is a physics based 3d tabletop that allows you to play a huge number of games thanks to a passionate community that implements and provides these via the Steam workshop. You will find just about everything here. The main downside (to some) is that game rules are not implemented or enforced. It's primarily a 3d simulation of the phyisical components. Many games implement some level of assistance using the built-in Lua support, for example they might automate setup or have a button for end-of-round cleanup. But generally it's up to the players to follow and enforce the rules of the game. I don't play a lot on TTS but I use it all the time to get a feel for a game or its components.
• Tabletopia is a web-based alternative to TTS with the same caveats. Smaller selection of games and less flexible UI, smaller (and less involved) community. Some games can be played for free, others require a subscription.
• virtualtabletop.io - is an open-source reimplementation of playingcards.io. You can think of it as a 2d version of TTS. I like this approach a lot, especially for card games or abstract stuff where the physics simulation and fancy graphics wouldn't add much. Relatively small but passionate community.
• Vassal engine - a Java based open-source desktop app. Lots of modules and a passionate community. Worth checking out especially if you are into wargaming.

Apps that fully implement the rules

There are a lot of apps out there, some for mobile, some for desktop (many available on Steam). Most require a purchase. The quality of implementations vary greatly. Some support online multiplayer, some don't or there is no playerbase. Some have nice snappy implementations, others have very poor UIs or go the other extreme and create an overly fancy UI that is too removed from the physical game. This is generally my least favorite option, I will almost always prefer a good BGA or Yucata implementation over an app. There are a few exceptions: Ascension, One Deck Dungeon, Onirim, Sagrada and Paperback are some where I like the app version a lot.

Mine:

• A couple of very cheap sectioned trays. Shallow enough to make grabbing tokens easy and enough sections to organize them. We use these for pretty much every game with tokens.
• A side-table to help deal with table hogs.
• A couple of those foldable dice trays. I don't actually use them for dice but as a flexible funnel when bagging things.
• Notepad, pencils, eraser
• An empty tea tin. I use this for some games where you frequently draw items from a bag because it's a lot faster.

Thanks OP for the excellent post, the BGG link markup is very helpful!

Sensible production and packaging choices would be a good start.

For pure teach Nithrania - Game in a Nutshell and JestaThaRogue are my favorites. For playthrough based teaches JonGetsGames is good.

Before You Play is kind of a hybrid, they often do a teach followed by a playthrough. BGG's gamenight (have to search for "gamenight") often has good teaches and playthroughs, especially when it's Dave Arnott's turn to teach. I also enjoy Slickerdrips' playthroughs, the teach in these is a bit more loose but still helpful.

When you are in a hurry 3 Minute Board Games or The Rules Girl can be helpful but these are not as thorough.

Is this a hit board game? The number of BGG ratings and rank (13648) don't reflect that. Does it stand out in some way from the multitude of similar games?

It's fun to think about which modern games could have existed in the middle ages or antiquity.

Component complexity is probably the biggest limiting factor. Some components would have been very difficult or impossible to produce. The available printing technologies is a major one. Depending on how far we go back easily shuffleable cards are probably out and cards with lots of text or complex symbology are almost certainly out. So are fancy boards. Simpler boards (chess or go grids, hex) are fine. Meeples, dice, coins, tokens, bags, cups are easy.

Rules complexity might be another factor since it would be more difficult to record and reproduce very complex rules. Some kind of thematic connection woudn't hurt either. I guess you could try to explain Star Realms as heavenly chariots :)

Abstracts are a category that works well since we have a bunch of examples of those actually existing. Simple dice games, bidding games, certain drafting games should work as well.

Some specific examples of games I like to imagine existing in the past are War Chest, Onitama and Azul. Thematically they would fit well, simple rules, manageable components.

I wonder which of the more complex euros could have worked. Perhaps a simpler version of Castles of Burgundy? Fewer building types to keep component and rules complexity under control. Or maybe something like Ra.

Ascension is my most played by far. It's one of the earliest deckbuilders and the first one (I think) with the river-style market which has been used in many other deckbuilders since. The developers have done a great job exploring various mechanisms in the expansions over the years and most of the content is available in the digital version too. My favorite sets are the ones that use Insight (the amber gems): Dreamscape, Delirium, Deliverance.

Besides the game mechanics the great art, music and the smooth app make it very chill and enjoyable for me.

I like it a lot! We play at two and sometimes use a fan made variant that pre-populates some of spaces with a dummy color. This tightens up the game quite a bit. I love the way the game looks on the table and the tactility of the tiles. This is a game where the production elevates a good game into a great experience. I only wish that the cards were standard size for easier shuffling and handling.

I've been thinking about different ways we could draft at 2p. For example a Biblios style draft where each player draws 3 cards one at a time and has to keep one, give one to the opponent and place one into the bonus area. Or maybe just an open draft where we take turns picking from the current batch of face-up cards.

If anyone has the expansion I'd love to hear you experiences with that, especially at 2.

I am guessing that it may be referring to this. Note that the post is on the Stonemaier site so it's their side of the story. Some searching also turned up a later analysis in a BGG thread.

In a hindsight given the extremely wide distribution, HUGE number of copies sold and many followup products all of this doesn't seem very relevant.

Example summary for Tiletum:

setup

• board:
  • populate action wheel with action tiles (optional) and bonus tiles
  • 3 bonus tiles for king track (no tile for last round)
  • bonus tiles for map spots based on player count
  • town and fair tiles on track, fair order marker on the picked towns
  • cathedral tiles and random build reqs. Remove unavail cathedral
  • contract and character markets
  • 10 dice in bag (2p)
• players:
  • markers on score track, turn order track, king track (p1 on bottom!)
  • place houses and pillars on their spots. There should be 2 of each left for each player as their available supply
  • 1 of each resource
  • 1 gold for p1, 3 gold for p2

play

• prep: draw, roll and place 8 dice (2p)
• action:
  • p1 flips and applies corruption token
  • dice values +/- for 2 gold. affects action and # resources
  • pick die, get bonus tile and resources, perform action
• king: points, bonus tile, player order. bottom wins tie. from negative snap to 0 after
• fair: merchant or house in town to qualify
• cleanup: refill wheel tiles, rotate wheel

Tasks (free actions) at any time:

• gain a resource for 2 gold
• fulfill contract
• place crest (food cost). Apply bonuses
• build cathedral (only 1 of each type!)
• use helper tiles from storehouse

Important:

• many house spots are only for higher player counts. With 2p there is at most 1 spot in each city
• some house spots have bonuses
• players can only get 1 cathedral piece per type!

(should add a section about scoring too)

Apparently I am "Expert" but I don't feel like one. I just like playing lots of games. I have too many games but very few unplayed. The "as many as you can" is bound by money, space and time to play.

Since you are on vacation and might not be able to find some of the other suggestions I will mention Liar's Dice, also known as Perudo. If you can't find an official copy all you need is 5 dice per player (so 30 dice for 6 for example) and some cups or other way to hide the dice rolls.

• Sea Salt & Paper is set collection with some rummy elements. Some simple but fun card abilities mix it up. One of our favorites. Available in the EU (Philibert, probably others too)
• in Cabo you are trying to minimize the value of your face down cards. Has a memory element but not too bad. Widely available.

I've been playing Challengers a ton on BGA. There is a lot more to it than it may seem at first and it's a very fun game.

Yesterday I was mentioning Azul as an example of a game that's very easy to teach and a lot of fun when played casually but at the same has great depth at high level play. I think Challengers falls into this space too. The award is well deserved IMO.

The Decision Space podcast has just covered the game if you'd like some more in-depth discussion. They rated it very high too.

Edit: I totally missed that Sea Salt & Paper got a recommendation too! It's one of my absolute favorite small deck games, very addictive! And I'd highly recommend Next Station: London too if you enjoy flip & writes. It has quickly become one of our comfort games.

Board Game Oracle has a prime day page that makes it easier to browse through it and lets you filter further by BGG rank and other criteria.

Some small games that stand out to me:

• Jekyll vs Hyde $11.99 excellent 2P-only trick taking game
• Silver & Gold $6.49 fun flip & write by PWH
• Bruxelles 1897 $13.99 (not to be confused with 1893, this is a smaller card game)
• Pandemic: Fall of Rome $19.99 is my favorite Pandemic (along with Pandemic: The Cure)
• Horizons of Spirit Island $14.99 seems like a steal
• Glow* $23.49 is a cool drafting and dice placement game with neat art
• Coatl $20.99 is a set collection and drafting game with fun components
• Spicy $10.49 is a bluffing game that works at all player counts. Kinda like Liar's Dice but with cards

My picks: On the lighter side Phil Walker-Harding. The game might be end up being light but it will be very likely enjoyable. On the mid-weight side it's probably Simone Luciani or Daniele Tascini or possibly someone else from the Italian-style euro designer group (T-series, Grand Austria Hotel etc). I've liked pretty much everything I've tried from them so far.

If you like Splendor and often play at 2 then Splendor Duel is definitely worth checking out. The new draft and new win conditions change things up quite a bit. I still like to go back to regular Splendor too though when I am in the mood for that pure Splendor goodness.

NerdzDay is an annual sales even by Gamenerdz, a US online retailer. It's very popular because they often include some very good deals and the store has a relatively low free-shipping threshold and an easy to use customer hold option (which means that they can can hold your orders until you pile up enough to qualify for the free shipping)

Worth clicking through for his discussion of the picks though, especially if you are not familiar with all the games. The podcast version is a good listen too.

I don't think that anything currently in alpha will show up since those are often not quite ready yet. But the beta list has a bunch of really nice games that I imagine might pop up: Evergreen, Canvas, Micro Dojo, Hanamikoji and Schnapsen are some of my favorites. Ginkgopolis is supposed to be very good too but I haven't played it yet.

edit, looks like I got Evergreen right!