When I weld up frames, like how you are framing up the sides and back, Ill tack all the pieces down to my fab table then weld them all together.. Even then it doesnt always come out perfectly square, but when you weld the back to the sides and to the bottom etc, you can rack everything to square before you fully weld it.. One thing you really need to concentrate on when welding this thin stuff is to not weld too much at one time.. Weld one inch, skip one (or two) inches, and weld another.. This will help tremendously in keeping the warpage down.. Also, make sure your heat, speed, and wire diameter is good.. What thickness steel are you using? 1/8" or 3/16"? Looks really good thus far.. Ill def be keeping my eye on this one..
Wheels.. HF has 10" pneumatic casters, both fixed and swivel on the cheap.. Im putting a set of those on the bottom of mine pretty quick.. They are pneumatic, but you can throw 'em on and then shop around for solid wheels to replace 'em.. The hold 400# a piece I think so they should be plenty stable.. Again, great job so far man.. Smart move on having your steel yard cut everything for you..