I had a cheap inverter for a while, rarely got used and was picky about input, it went to a friend, I've got my aged transformer for arc and that's more than I need, I have no really issues with using it and get more than adequate welds with it, can chuck it in the van and work in the middle of a field with it off a generator and it won't bat an eye. have a couple of mig units (kennedy and Kemppi) both are a pleasure to use but both are workshop only with occasional work on cars just outside.
Unless you are going to drop a further 300-600 quid you'll be scratch tig with it most likely which is an introduction but not really great in the long run and you'll end up spending 3-4 times that to get a unit that will do what you want.
for me, I'd spend pennies on a second hand transformer unit (because everyone wants rid), learn to weld with that then pass it on and get something better, but then, this is how I learned although I had access to some rather good kit, it was better to learn with what is now considered hard kit, made everything else seem easy. Maybe I'm biased. you are going the wrong way round from the norm too, most people start with arc, move to mig then on to tig. don't need to do it this way though, just the way it seems to go.
oh and they are off the peg, retailer picks his brand by the colour type of kit, so look around, if you want an invertor you'll find it cheap in other places depending on your desired colour.
someone will be along shortly to tell you I'm wrong and don't bother with the buzzbox it's to hard to do.
