TIG ,MIG or stick for SS, depends on the finish you want.
With welder ownership, TIG, you will need a TIG welder and rent a gas bottle of Argon for ever. With MIG, you need a MIG machine with wire feeder (expensive) and you can get gas-less wire for mild steel (welds look crap), but if your welding SS, you will need to rent a gas bottle of Argo-shield for ever. With stick, you just need the sticks (welds look crap until your a legend welder).
If your creation is indoors and you don't need to earn a living from the equipment you will need to buy, I suggest a mild steel frame, stick welder, then grind/sand welds and paint mild steel frame with gal paint.
Other option is to just find a place that does the SS welding and pay them in cash or grog.