Why not both? Not gonna be cheap to get a reputable multi-process unit though, Lincoln have some compact ones starting at around £1200, Millers are another £500 on top of that.
Also an option. I have both. 2 TIG, 1 MIG. But for the price of a single unit that can do both, you can get two separate units and have change left over.
Which one, MIG or TIG? They're very different beasties. What do you want to use it for? TIG is much, much more expensive than MIG.