The turbo commonly referred to as a "k03s" is a transverse turbo, ie it only fits A3/Golf platform cars.
As for required mods...
Decent front mounted intercooler and a 2.5 or 3" downpipe with sportcat is a good starting point.
As for the turbo itself, instead of buying a proper K04-015, you can modify your existing K03 (or i can sell you a standard turbo you can have modified and then install)
You want the exhaust housing machined out the take the Turbine wheel from an S3, then you have a few options on the compressor side, either keep the existing housing and use either an RS4 compressor, or a 2077 ETT wheel. These will be good for around 240hp. If you want more, then you can use an S3 compressor, housing and backplate, which probably gives scope for around 260hp.
Your choice of turbo will then dictate further mods.
The original MAF maxes out around 230-235hp, so if you go with the smaller compressor and accept a max of around 230-235 then you'll get away with only an injector upgrade (C20LET Yellows)
If you want to push for 240+ then you'll need to upgrade to a 3" MAF housing.