Since your car is a '96+ Civic, you must reuse your Civic's on engine harness. This isn't much of an issue except there are places it won't plug into the new engine, specifically the one's you mentioned, distributor and injectors. You can either use B-series OBD I versions of these or find a way to make it work (injectors would just need the clips, I've heard of the distrib being rewired to work but I don't know what's involved, there will probably be others). Your also obviously going to need an OBD I ECU and an OBD II to OBD I conversion harness (if you use your '96's engine wiring harness, OBD IIa or '96-'98 OBD II). You can't use an OBD II computer because the new engine won't have sensors the OBD II ECU requires (specifically a second O2 senosr and a CFK sensor).

That's the mechancial parts, the legal issue is different. In CA, you can only use an engine that's the same year or newer than your car (and I'm sure the rule continues to other states even though it's dumb). Also, by using an OBD I ECU, the diagnostic port under the dash will no longer function. Some emissions/inspection places sometimes hookup to this to check for codes before testing a car, and will fail you if the ECU doesn't respond. You don't list where you live but rules are different for every state and even every county sometimes. Check with the local emissions/inspection place you'll end up taking your car to to find out what hoops you have to jump through, if any.