A 130A MIG that runs on 110V wall power is going to weld up to 1/8" steel material thicknesses with one pass down one side of the material. It will also weld 3/16" or 1/4" steel material if you weld two passes, one weld bead down both sides of the material. A 175A MIG which runs on 220V power will do 1/4" with one pass, and 3/8" to 7/16" with two passes, on steel.
Don't confue a MIG with a wire feed welder. A MIG technically IS a wire feed welder, but it has a shielding gas. The el-cheapo wire feed welders from the Home Depot type retailers typically are called MIG welders, but really are not, because they don't have the shielding gas available as purchased. Read all the box and see what's included. I've used the flux core wire in my Lincoln SP100 (predecessor to the SP135 Plus, purchased in 1992), and it welds kind of crappy. Most of the flux core wire if just too large a diameter to weld nicely with the 130A machines.
Just starting out, the 130A MIG which runs on 110V wall power will do most things. Many people don't like them, but frankly, I've welded more stuff with my 130A Lincoln than you could imagine. Sure it's not going to weld 1/2" material, but I knew that when I bought it. It's the equivalent of trying to push over a 400' tall northern CA Redwood with a CUT. It just won't happen, and was never intended to either.
I've never used the stick welder attachment that came with my TIG, so I'm not going to comment on it. You probably don't want the TIG if you have never welded, and it's out of your price range anyway. Frankly, I suspect all the decent MIGs are out of your price range as well. Now the 175A Lincoln Square Wave 175 Pro will weld 3/8"-1/2" with one pass, no problems at all. Lots more control on power and rod feed though, given that the rod is fed by hand, and you can leave the torch in one place on the puddle and let the puddle penetrate.
Maybe I need to try the stick welder attachment. I've owned this TIG since about 2000 and haven't even removed the stick clamp from the bag.