Get yourself a TIG torch, a bottle of gas, hoses, and a power block and learn how to run a dry rig. That’ll get you your thin stuff way better than a MIG machine. Run some 3/32” 7018s for the rest of what you’re describing.
For those who‘ll go out and say you can’t TIG weld outside, it’s a bunch of malarky. Build something around you to stop air movement. All you need is a couple of tarps & something to hold them up. Been there, done it on more than one occasion.
If you really want a MIG machine to run off a drop cord, Lincoln has their 140 & 210MP machines, and I’ll personally vouch for the 210MP being a great machine. Miller has their 211 which probably works great too.