Going 18650s, you don't want to buy crap cells, or laptop pulls, or cells that have been stored incorrectly (full/high/low temps,) so $2 a cell is a bit spotty. For $5 a cell, you can get the newish 3400mAh Panasonic NCR18650Bs, which have been at the top of the heap for 2-3 years, although they aren't >10A drain, that shouldn't be a problem for your setup.
If you want 10A cells, but still almost as high in capacity, you might try the Samsung 30Q, the LG MJ1s and/or the Sanyo-Panasonic NCR18650GAs, but those will probably be over $5 in say quantities of 20+?
If you go 3S8P: 3 in series, 8 strings in parallel, that'll be 24 total cells. They come hot off the charger at 4.2v and are 3.6-3.7v nominal, so we're looking at 10.8v (nom.) to 12.6v. Throw in another in series and you're at 14.4v-16.8v and then capacity will be 3400mAh x 8, or approximately 27Ah.
You can play with the numbers and amounts.
You'll need a balancing charger, since you're charging in strings and that implementation is probably a bit above my pay grade, but guys build 50 cell packs for electric bikes everyday, so it's being done and done safely.
This guy might be able to help you, if you PM him:
http://www.candlepowerforums.com/vb/list.php?author/10167-Overclocker
Here are a couple of good places for li-ion cells:
https://www.imrbatteries.com/
http://liionwholesale.com/
There are E-bike sites out there, as well and building packs and charging solutions are their speciality.
Chris