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I would do an R134a system and use the TRS90 compressor with the DelSol VTEC AC bracket. Not sure about the B20 bracket.
I'm not sure what condenser came in the EG chassis with the R12 system - if it's a serpentine flow condenser, you'll definitely want to change that out to a parallel flow for the R134a. Clean out the system to remove the mineral oil and use PAG 46 oil.
The problem with the EG civic AC system wasn't the compressor...it is the woefully small condenser. As @DaX mentioned, get rid of the serpentine condenser and get the parallel flow.
When I rebuilt my EG, I put in a Denso/Sanden TRS090 brand new...NOT a reman. I got a line set from a 95 Civic that used R134A. Cleaned them thoroughly and dried them. Replaced the entire evap coil and expansion valve..so it was essentially a brand new, dry system. A heads up, the Integra units used a 10PA15C style compressor. These will work on a swap, but will require additional work with the line set as they aren't exactly plug-n-play with EG lineset.
The B20 (P7J) bracket will fit on a B series and mount D series compressors...however, the clearance between the frame rail and the mount stud don't exactly play right (At least on mine it doesn't..i don't have it connected to the frame there and it does kind of bother me).