$500 would be heaps for a decent stick welder, and in some cases would go most if not all of the way towards funding a TIG torch for a unit which can be run in Lift-TIG mode. Something like a 17 series air cooled tig torch would be fine.
$500 on the mig side would work, but Ideally (and I say ideally, because if you are working on home jobs, it'll get you down) you'd be looking for a synergic (1 dial) machine. The old 2-dial jobs can be a bit more finnicky to set up for your particular job. The synergic units have 1 dial- you choose your voltage, maybe around 19V for a 0.8mm wire, and the wire speed is matched to that. You can throw in a voltage trim to adjust the heat input. Also having an inductance (choke) function will help tune out spatter generated by the short circuit condition which occurs in MIG when the wire touches the weld pool and throws globules of spatter everywhere. The choke/inductance control will prevent the rapid current rise of the short circuit condition and calm things down a little (although this happens multiple times per second).
One thing to note in MIG welding is the Amperage is a function of the contact tip to work distance- CTWD, or wire stick-out, which is often called amps on some machines. If your wire stickout was a rediculous 3m, you'd not even get the wire to melt when the welding circuit was closed. Likewise, too short a CTWD will vapourise the wire and be too 'hot'. Imagine a fuse exploding... same thing.
I can't comment on a lot of the machines out there, as I've never used them. Some I see have some scary stuff going on with them. One I looked at has a 10A plug fitted to a machine that idles away at an effective current of 30A... 3x higher than the circuit breaker in your power box, and well and truly in the melty wire / electrical fire red-zone...
Shoot me thru via pm something that might interest you and I can offer an opinion.
Also if you don't mind buying used, keep an eye out for something that is a quality brand, operational and recently serviced... they do come up, and can be good pricing.

