I highly recommend you go to a search engine like Google.com and do a search for B16A and you'll find lots of good info, more than I can type in a few minutes. Just some quick pointers.

You'll need a mount kit to mount a B-series engine into a EF ('88-'91) Civic. HASport, Place racing and others make them. Do some research and find which one will work best for you. Contact the manufactures and tell them your intentions (turbo) and see what they recommend. I can tell you everything is going to be tight, but it can all fit.

As for the B16A's, there are a lot of differences. The B16A or B16A1 (same thing, just depends on who's talking) is the first gen B16A imported from Japan. This is the motor you want. It will have the wiring harness, ECU and tranny you can use (pre OBD and cable operated). First gen B16A's are usually around $1500-$2000. The B16A3 is the Del Sol DOHC motor and sometimes called the 2nd gen B16A's that are imported from Japan. You could use this motor (which has a little higher compression in JDM trim) but you will need to convert it to pre-OBD, find a pre OBD ECU and a cable tranny, it's also usually about $2500-$3000. The B16A2 is the '99+ Si motor. You could also use this, but have the same issues with the OBD system and tranny as before. These are usually more expensive simply becuase they're newer. For your application, I would recommend a B16A1, first gen JDM engine, make it easier on you. Make sure you do plenty of research and know everything beforehand to avoid paying to much money for stuff you don't need or getting stuck halfway through a swap. Seeya.