Theres no way to do it -CHEAP- and have a good setup imho... however, you can cheat, and just buy the RIGHT parts the first time, and keep it to a bare minimum.
So... to a -stock- car, here's what i'd buy:
Turbo (This is the most important purchase... don't slack on it, and buy a POS cheap thing.. buy it right (and no, that does not mean cheap)). Maybe spend about $7-800 on a basic turbo with internal wastegate (important for budget setup).
EMS - Either TurboEdit, or ZDyne Gold SECU.... nothing else, unless you want to convert to OBD1, then Uberdata or Chrome. Lets shoot for the high end, and say $600 or whatever it is now for the ZDyne.
Log manifold and DP from a REPUTIBLE manufacturer. I think you can get a setup like this for about $500 or so for both.
450cc Mitsu injectors... not 'ideal', but they'll work great... can get them for between $50-100.
Oil feed and return kit - Expect to spend probably about $125 or so i think... dunno, i haven't bought these retail in some time. look for a place called StealthMode Performance... last i heard, they had good prices, and the proper steel fitting for the back of the block.
charge piping - This could be anywhere from $50 to $600, depending on materials and your own fabrication ability.
intercooler - Again, this can vary, but even some of the cheaper eBay ones work well. I guess expect from $250 up to $500 for something purty decent.
Thicker Headgasket (Cometic) to lower CR - $120
ARP Head Studs - $100~
blowoff valve - for low boost, a DSM one will work... expect somewhere around $25-40 for that.
Misc clamps and connectors, vacuum line, and stuff - Budget about $200 for "stuff"
At this point, you have everything you need to put together a reliable setup for low boost. Notice there is no wastegate other than the internal one on the turbo.... that'll work just fine. also, of note is there is no fuel pump. The stock pump will work fine up to a point, but when you do a modified pump, also do a FPR...
Anyway, so this totals $3385 (i estimated $300 on average for charge piping)
So that is MINIMAL, and it is over $3k, with no labor involved. However, this is what i consider minimal... after seeing people having SO many probalems with those bastard eBay kits, and throwing their money away and hurting their motors with cheap turbos, and mis-management of their fueling and ignition, i'm not about to recommend anything cheaper.
So for less than $3k you ask? won't happen imho, without getting stellar deals on stuff, and even then, those "deals" can EASILY come back and bite you because you wind up buying cheaper parts just trying to save a few bucks.
With a good turbo setup, you can go quite far with it though, especially on a B16. My old B16 with stock bottom end and good management survived happily at 16psi, making just over 300whp with a bitty T3 turbo... it was FUUUUUN!