I second Metal Supermarkets. I have used them several times for small order stock since I have one locally, only about an hour drive away. For the store I use here in the DC area, I have noticed a price difference between ordering online, or just calling them to order. Calling is often cheaper prices per foot for some reason....not sure why, just keep that in mind. I used to use onlinemetals.com, but their service went to crap when they got bought out by one of the big names several years ago. Haven't used them since.
Also see if any local scrap yards will let you pick through their stock. I do this often, and will frequently score some nice AL and SS drop offs for literally pennies on the dollar. The main scrap yard I use which is just down the street from me used to have a contract with one of the Navy bases several years ago to handle all of their scrap. Beautiful 6-8 ft long drops of AL, SS, and brass in varying dimensions and types...guess the base didn't want to keep those lengths for some reason. It was so plentiful that I eventually started buying most of it up, cutting it up on my bandsaw into shippable lengths, and selling most of it on Ebay if the alloy was clearly marked. Made thousands doing that, and of course always kept some of the stock for my own inventory. It was a sad day when they lost that contract and most of those pristine drops dried up. Sorry, I got off topic...
6061 AL would be a good choice for practice. Thickness depends on the capability of your welder and what you intend to practice for. You probably can't go wrong with coupons that are 2-4" wide and 6-12" long. Good general thicknesses for practice would be 1/8" for the most part, with some 1/16" and 1/4" thrown in there as well to test your abilities. Once you get good with those, try some stock that is even thinner/thicker to see what you can do. 1/8" would be the best starting point for practice, IMO.