What's the biggest consideration here? Cost, utility, being able to hook it into a 110V plug?
You can change the plug on any welder you get, to hook it up to your existing 220V circuit if necessary. Briefly looking, for instance, at the Hobart Handler 190 (which is a great little welder for the money), it's showing input Amps at 220V being 20.5 to meet the duty cycle of 130 Amp 30%. Max power tap (setting) on that machine is 190 amps, so you'd need a 30 amp circuit to probably run it full blast without tripping the breaker, but when I had my 187 model, I'd rarely run it higher than the 4 or 5 position tap, which is about half capacity, for tacking billets and sticking general shit together around the shop. You only need max power output for single pass welding of the thicker stock rating, which is 5/16". Of course you can weld thicker stuff with different edge prep at lower settings (within reason), and multiple passes.
Ultimately you'd probably want to run another circuit, I'd recommend going ahead and putting in a 40 or 60 amp circuit in for a welder, typically it's one of the clothes dryer type plugs (a lot of people use their dryer circuit if their shop is in the basement or garage near it), but if you've got that existing one, you can use it.
You'll have to experiment and see what the power limit on a similar welder would be, but I'd bet you'd be covered for a time, before you learn to push the capacity.
Stick is cheap and easy, but it's often dirty, and requires experience and lots of prep and other variables to be right, to get good structural welds. TIG is the most versatile, if you've got an AC/DC machine with the right accessories, but it's the slowest to setup, use, and takes a lot of practice to master. I have a big powerful old 300 amp tig welder, takes up a lot of space (I'd like to replace it with a compact inverter TIG), and honestly, rarely gets used. I bought it for doing the filler-less tig welded dry stack welds, but found out I could do the same thing, much faster with mig, so the only time the tig gets pulled out, is when I need to weld stainless or aluminum, or do "pretty" welds on steel, or something else complicated or semi-delicate (my machine isn't great for doing super fine work on sheet though).
I did a bit more research, and it still seems that while inverter TIG can do some pretty interesting stuff on the higher end machines, most of the dual voltage MIG machines still seem to be "not very great" at 110V.
Under any circumstances, it seems like you'd be better off hooking up to that existing 220v circuit, if you can't run a new one. Are you in a residential area with really strict oversight? I personally always do my own electrical work (it's not difficult, once you understand the safety considerations), but if you've got liability concerns, it may be well past time to develop a relationship with an electrician, most of them like knives in my experience. Paying for electrical work can be expensive, but dropping a short run 220 circuit for a welder is an easy task, even if you do have to hire a stranger, just shop around, but I'm willing to bet, a knife to the right guy, and you'd get it done for free real quick. Only major material cost is the wire, which even if you run a large circuit for a hypothetical "cover all your bases" in case of a big welder in your future, if your breaker box is reasonably close, material costs could be less than $100 total.