Hobart , Lincoln,Esab,Rediarc, Miller and there are some others out there now as well, make some very good feature packed/compact economy inverter style tig welding machines that will fill the bil for you.
I have seen some amazing stuff from the current crop of 110 volt inverter type power supplies.
It just depends on what and how much you are going to do.
Any low end machine is going to be short on features you will want later on.
They are ok you just have to realize their limitations.
Look first for some good used equipment that still has manufacturer parts & service support.
You might find a bargain on a more feature packed machine.
The ideal is to get a unit that is a good power source that you can build around/expand as your requirements change.
We have a machine at work that that is an older POWCON (no longer made) inverter style unit that does stick, mig, tig & plasma cutting. The only thing it lacks is the high frequency provision required for tig welding aluminum. Very versatile machine in all other respects and great for a repair facility.
A Miller SynchroWave 250 (my favorite) is a Caddillac unit that does it all except plasma cut but they are rather large and expensive.Nuthin'ike a liquid cooled tig torch handle though.
Mig lends itself very well to production high speed welding where you are fabricating just one type of metal for long periods of time.
Mild steel all day long , no problem.
With mig everytime you change materials you will have to change out the wire spool, quite possibly the shielding gas and in the case of aluminum also the gun liner.
Tig gives you more control over the process ,is more precise,cleaner but is slightly faster than traditional oxy acetylene gas welding but without all the excess heat. The way you feed the rod is just like oxy acetylene style welding .Heat/amp control on the torch handle is nice for out of position welding where you cannot set up a foot pedal position.
You will still have to have different sheilding gases for the different types of materials you plan on joining.
Steel,Stainless Steel & Aluminum usually weld best with a gas mix formulated just for that metal.Argon is a safe bet for almost everything but aluminum usually requires helium or helium/argon mix.
The beauty of tig is you can keep a lot of different types of rods around so changing materials is not as big a chore as it is with mig.
Different materials require different types tungsten electrodes for the tig torch.Aluminum does best with rare earth tungsten electrode.
If you plan on tig welding aluminum you want a machine that will:
1- have enough amps to do aluminum because aluminum dissipates heat much faster than steel
2- have some sort of high frequency or "hi frequency start" provision for doing aluminum."scratch" start(ok for steels) for tig on aluminum sucks because it contaminates the tungsten and can give you less than perfect welds.
3- have a post flow timer on the purge gas so purge gas flows onto weld area for a preset time when you stop.