I would think a 110v welder like the Hobart Handler 135 would fit your needs. I mention that welder as I have one and it does all as advertised. Lincoln-red, Miller-blue, and other colors will probably do a fine job too. 110v welders work OK on a breaker w/ wiring/ & w/ an outlet heavy enough to handle the little machine on it's highest output. I use self -shielded fluxcore wire (E71T-8 or E71T-GS) in mine without a hiccup. I have the gas regulator w/ bottle and never ran any solid wire through it, although I will, at some point, as needs arise. My father-in-law and myself have built many homemade trailers using nothing more than that welder and a buzz box with 7018's. You can handle thicker materials than the 1/4" that you are limiting yourself to, by simply running more passes. It adds more time to your project to run more passes but it can be done. You are limited to a 3/16 fillet, at best, in one pass. I know you mentioned you didn't like the fluxcore wire, but it will handle dirtier materials than the solid mig wire. What I mean by dirtier is that it will burn through mill scale and rust to a certain degree where as the solid mig wire (ER70S-3 or ER70S-6) is fussier about how clean your material needs to be.
A few thoughts for you to consider,
John Wright