i have the b16.. its actaully really cheap to buy motors and do a swap into a 90-93 da6. first of all, you can use your stock tranny, ans axles and the motor bolts right in. second of all, its cable, not hydro tranny so the tranny is half the price of a hydro if not cheaper.
i bought a j1 tranny for $250 in so cali, found a b16 for 450, and got the ecu for $200. all in all they were decently cheap. still, im sure you can find a good b16 cable tranny conversion cheap. if you wanna get a slight edge, buy a ecu harness converter and go obd1 with a p28 and a mugen program. i think there are better programs for obd1 then the obd0.
if you buy a gs-r full swap, you will not need the axles, or tranny, so you have to find someone to buy them, or just buy the engine by itself.
shouldn't cost you more then 2g's to have a nice running fast car. b16s are still really quick in an integra. you can hit at lesat 140 at the wheels stock. use some money for a dc header and intake/ exhuast.. you'l lbe having fun. good luck