It sounds like your doin just what i did, only my civic is a 91 lol. my friend wrecked his 94 teg so i pulled the b18b1 out of it, and it was also an automatic lol.
i'll just list everything you'll need regardless of whether you know you need it already or not lol
-B18b1 obd1 engine
-Manual trans P75 obd1 ecu
-Trans of choice
-Integra axles (90-93 non-abs)
-90-93 integra MANUAL intermediate shaft
-P75 manual integra ecu
-Rywire obd0-obd1 conversion harness
-DA throttle cable
-shift linkages (ebay, avid, innovative, hasport, etc)
-new/resurfaced flywheel and flywheel bolts
-clutch kit
-Motor mounts (ebay, avid, innovative, hasport, etc)
-B18 manual tranny starter
-B18 cable tranny speed sensor (assuming you want to use stock gauge cluster)
-90-93 integra drivers side engine post bracket
-90-93 integra rear transmission bracket, must be from a manual
If you have an si, ex, or dx you're fine with axles. if you have an hf or std, then you need to swap spindles for the da axles to work.
If you intend on using obd0 injectors you can leave your resistor box alone. i however would recommend using the ob1 injectors. splice from your donor cars harness onto your obd0 harness the proper obd1 injector plugs, and then swap the obd1 injectors over. then remove your resistor box. solder all 5 wires that are on the engine side of the harness (4 red/black, 1 yellow/black) into eachother and then wrap the whole thing up in electrical tape.
be sure to pry the dust covers off the back side of the hubs to allow for clearance of the axles, if you don't remove the cover they may bind up causing the axles to prematurely fail. heres a pic showing removal of the cover, its quite easy just use a flat head screw driver to pop them out.
You'll need to move and extend your coolant temp fan switch wires from the back of the block to side of the head on the thermostat housing. its a two prong plug with one single-wire connector on each. just cut off the connectors and solder/barrel connect the proper 2-wire fan switch plug from your donor car to these two wires. if you don't get this hooked up your radiator fan will never kick on.
Also you will need to make a dent below your driverside frame rail for alternator clearance. if you dont the alternator pulley will rub against it.
You can use the radiator hoses from the teg, just trim them to fit. they're a tad big for the upper and lower radiator connections, but if you tighten em down tight you'll be fine. mine haven't leaked yet. and lastly just unplug your map plug from the firewall and snap it into your new throttlebody mounted map. and the vaccum lines are pretty easy to figure out once you take a look at where everythings going.
And that should just about do it
