120 GMAW machine can usually go to about maybe 14-16 gauge steel sheet. That's it.
Some 0.035 FCAW wire and those little 120V machines can go to maybe 1/4 inch thick steel.
The 180-class 240V machines can usually get to about 10-12 gauge GMAW (about 1/8 inch thick). FCAW, they can go to 1/4 inch or maybe 5/16. Thicker than that you really need a bigger machine or to break out the SMAW (aka stick) machine.
$400 budget? That's the tough part. You are then looking at used machines and/or 'import' machines.
And I agree that 'starting out' with a 'cheap' machine can be frustrating, as you aren't sure if any problems are from you or from the machine.
You'll absolutely need some welding gloves. That's maybe $10-$20 per pair or so.
And a helmet/shield. The HF low-end autodark goes for about $40 on sale, seems to work OK.
Grinder (or 6

). Some wire wheels to go in the grinder. Some grinding wheels, and some flap disks.
Shielding gas (cylinder + refills) for GMAW ( usually C25).
Electrode wire. Solid and/or some FCAW for the 'thicker' stuff.
Some metal clamps. C-clamps, bar clamps, F-clamps, welding magnets, etc.
Some way to cut the metal. Hacksaw, jigsaw, sawzall, zip-disk in the grinder, plasma

.
The $400 budget is tight, especially if you need to get a bunch of all the 'other' stuff.
The Hobart wire-feed machines have a pretty good rep, good machines.
Lincoln, Miller, ESAB as well.
Something to think about. Consumables. By me, if I need to get some 'standard' contact tips or a nozzle, I can get the small Lincoln stuff at Lowes or HomeDepot or Walmart if need be. Don't have to go to the LWS or order something and wait a week.
For wire, some of the really 'small' machines can only take the little 4" diameter wire spools (1-2 lbs of wire). The cost/lb of the wire there can be 2x of the same wire on a bigger 8" spool (10-12 lbs of wire). The bigger industrial-type machines can usually take the big-boy 12" spools (33 or 44 lb of wire) which costs much less per pound than the 'little' spools (but you are buying 33 or 44 lbs of wire instead of 2 lbs

).