Oh man, if you have a Lego store anywhere near you then you are in for a treat! Every store I've been to has a literal tower of bins that are filled to the top with Lego mini fig parts. You can custom build you're own mini figs exactly as you want with one caveat: They may not have the EXACT piece that you are looking for but coming up with your character with some limitations is half the fun.

My personal favorite that I have created is Minifig Richard Hammond:

If you are artistically inclined at all you could look into Titancraft, Hero Forge, or Eldritch Foundry. They have online custom miniature creators, some will print them for, and some will even paint them for you.

This is the one I've heard used most. It's got everything from full sets to individual parts. https://www.bricklink.com/v2/main.page

If you aren't sure what piece you are looking for but know what set its from you can look it up on this site http://www.peeron.com/ and then search bricklink by the piece item ID. Hope this helps

Bricklink or Brickowl. And you can find non-Lego branded ones on AliExpress.

In addition to the other solid recommendations I would like to add Bricks and Minifigs stores.

You can order them online through the LEGO.com store.