I have never dabbled in auto swaps, But it should be straight-forward if you stick to the OBD of the car you are swapping into
since your car is obd1 you should be looking to get a swap from a 1994-1995 integra, this way you can get all the right parts from one car
You will need:
The engine (with the mounts)
TRansmission (also with the mounts)
shift cables
axles
ecu
engine wiring harness
This is a very straightforward swap because the civic and the integra chassis' are nearly identical so everything plugs and bolts right in
the only 2 things you may run into a problem with is the wiring for the o2 sensor, some of the early obd1 civics (1992 and 1993) Only had a 1 wire o2 sensor, while some came with a 4 wire. With the integra engine and ecu you will need to use a 4 wire o2 sensor, so check your car to make sure it is already wired for it.
The second thing is that some civics came with a firewall mounted MAP sensor as opposed to a throttle body mounted MAP, the way to check it is to look at your throttle body that is on the d15, on the top of the throttle body there should be a sensor that says "map assy". if the sensor is not there then look at your firewall directly above your fuel filter, and you should see it there. what you have to do is if you have the firewall mounted MAP, then you need to simply extend the wires to the MAP on the integra engine once you get it in the car.
Hope this helps, if anythign is confusing, just post back.