I think if it's a case of one or the other I'd go with the TIG. As been mentioned, TIG will get you out of a lot of tight spots in mild steel, ally and ss so it's pretty versatile. If you have a lot of mild steel welding though in terms of a large frame then MIG is twice as fast and simple once you get your set up and angles right.
However if it's an outside job on a windy day, welding gate posts etc.. my ancient Pickhill Bantam kicks ass everytime. (Once you have someone to reset the trip after the inrush into the coils knock the mcb).
Still for a lad with a workshop or garage I'd still go for TIG. The control you can achieve lends it to many applications. Even putting holes in work hardened stainless when someone calls over after trying to drill a hole in ss with high speed on their battery powered drill....(clamp a heavy washer around the hole first to limit the burn.)
Definitly agree about gas bottle rental. Don't dream of taking out a rental contract on your bottle, even the small ones. Pick on up second hand is your best bet.