Miller, Lincoln, or Hobart. 110 will work for hobby fun and basic welding. Thickness is limited and wire feed w/o a gas shielding brings more contaminates... however, for fun welding, mig wire feeds are a fun entry. Picture a glue gun - in this setting your pushing (or pulling) a puddle of metal. I dig the heck out of it!
Buzzboxes (same order of preference) are another option for 110. AKA Stick welding - Fun hobby with slag that is brushed off. The slag is a sort of shielding while the stick is running its bead.
Both are in the same price - general area for starters. I think Buzzboxes are more capable unless you hook up a gas shielding to the wire welder - If that route wire is the better route (IMO - of course)
If you can bump it up a bit with argon mix gas shielding for your wire welder selection - that would greatly improve the weld integrity. If you bump it up to 220 - w/ gas, you're ready to rock and roll with just about anything the welder is capable of throwing down.
Welding is fun as hell!
Edit:
Sorry got carried away and skipped your Q's: YMMV and this is simply IMO:
Anything going on a highway or involved with others around - I would not go with a 110 gas-less welder. If it's to build a go-kart for personal fudding around, it's still borderline on it's use. Others may disagree. It basically boils down to the integrity of the weld. If the integrity is compromised, the more likely the weld is to fail. Shielding of the weld is paramount for anything involving personal security/safety.
Thickness of metal for a 110 - maybe 1/8 - 3/16". I wouldn't trust it beyond.
Plasma is a separate component unless going higher dollar then options for other attachments are present, such as plasma. Though in most cases, (IMO) plasma's are their own unit.
Get into 220, and aluminum wheel guns are a boom! fun lightweight fabrication.