Assuming your car is a manual, this would be much easier.
The following information is just what i've collected over a few months of reading thousands of threads/info/talking to people who've experienced this. I have no first hand experience with this myself so my info may be wrong on some points.
If you're on a budget and don't want to spend more than $2,500 , I'd go with a Eagle/Vitara D-series turbo build. Source out a local D-series block , assuming your head and transmission are still fine. Maybe get a d16z6 or d16y7/y8 engine (whole engine+transmission if you want) or just block alone for under $100-$200 I don't know what the price is in your area. All you'd probably need is a good block.
Honda-tech marketplace forced induction section will be amazing for the following unless you can find parts locally, then next to that for information on a turbo-d-series build, refer to
www.d-series.org.
Buy vitara pistons, eagle rods, acl bearings, ARP studs, machining/measuring done at a machine shop *you want the right micrometer measured specs) torque everything down and you got a low-compression block that should have cost you under $600 parts and labor I believe.
Fuel management upgrade would be
Walbro 255 Fuel pump $100 new
440cc DSM injectors $60-$100
Piece together a turbo kit, ebay kits will run you maybe $800-$1,000 but those ebay exhaust manifolds and turbo internals aren't the most reliable. If you can do it right, you can get a nice kit of used/reliable parts for $700-$1200. That includes, but is not limited to. Turbo manifold, turbo itself, oil lines, wastegate. bov, intercooler + piping, etc; I'm not too sure of all this as I did my research and ended up putting this plan aside.
Then you'll need a obd2-obd1 conversion harness $50-$80 or you can DIY
OBD1 ecu,i'd go with a vtec one from pherable that already comes with a basemap, should be $100-$160
Then there's tuning, which is quite costly, but you can do it yourself with a wideband o2 sensor, a chipper, and a free program called Crome. There's a bit more to this however.
Then there's the little things that you'll need along the way like paying for shipping, engine rebuild gasket, tune-up parts like spark plugs/wires/dizzy/coolant/oil, etc;.
The good thing about Honda's is that:
1) Their aftermarket support is HUGE
2) There are thousands of tutorials online for almost any setup you want.
3) They can have great power from 200-500hp turbocharged and still be making 25-35mpg. Take that STI!