With out a doubt tig. I use a mig machine from time to time at work and I view it as a hot glue gun that works in metal. Messy spatter and not really good for making things like small tanks, suspension pieces, various mounts, and most small fine work. Just the kind of stuff I have been making throughout my SLC build.
Difficulty? I just don't think that there's all that much difference. You will need to prep and fit all the parts the same way which is a lot of the work either way. Then you are going to practice a bit with both machines. In the end you will learn how to use what ever you but and once you have a tig machine you can do anything. I don't fell that way about a mig.
Lastly mig's do tend to fool you as far as penetration goes. It's pretty easy to make a nice pretty bead and have it be cold and not adequately penetrate both pieces.
I have a 225 Lincoln. It runs off of a 50 amp 240 breaker and is about the max you can run off of normal house breaker panel. I have welded 1/4" Alum plate onto 2X6 inch 1/8 tubing when I did some changes to my SLC. Most of the time I was at about 160-175 amps. It's pretty hard to come up with a bigger heat sink than a RCR chassis and the Lincoln 225 had NO problem handling that.
Don't buy a 110V machine. IMHO it's a waste of money and you will be back for a better 240 machine later anyway.
My complete setup came in at $2300ish, welder, tank, regulators , cart, helmet, gloves , the works. I have paid for it at least twice over by now and I wound change a thing. The one thing I may add is a water cooled torch. The air cooled torch I have does get hot if you have long runs of more than a couple of feet to weld above about 100 amps or so.