If you have the budget (new OR used), I highly recommend the venerable "Lincoln Lunchbox", being an entire series of small, portable 120v wire feed/ gas convertible welders, starting with the weldpak 100, migpak 10, or whatever the he// they're calling the basic model these days. Please note "Lunchbox" is a nickname, you'll never find a model or series so branded. They're very functional, and durable too. I spent years beating the crap out of them, exceeding the duty cycles by retarded amounts and working in inclement weather. Excellent bang for the buck. For that matter, you won't go wrong with the Miller and Hobart equivalents. There are offbrand machines out there, from retailers like Harbor Freight and Princess Auto. They tend to be a lot cheaper, at the expense of quality and features. Some of the cheapies are non-convertible or have fewer heat settings. Sometimes Lower duty cycles. This might be okay for you, just wanted to point out a couple things that may not be obvious to a first-time buyer. Basically, if you wish to run flux-core (non-gas) just make sure the machine you want will do it. (which is likely, as a true MIG requires things that would drive up the cost) As far as the heat settings go, you may be okay building a kart with a 2-setting machine, but it will be a lot more useful to you with 4 or more.
Cheers- Chris