the b20b is a heavy motor...i have spent some time in the race / drag circuit and in my opinion, all that extra weight will counter the performance of a civic as light as the 88 model.
it can be done for sure but i wont rock it....if im building one for the track / drag...i will put as first choice the type r B18C and then turbo charge it. The best way to do it is to build it also at the same time while you are at it.
If a b18 is hard to get...b16 is a good choice as someone said up there....slap the turb and put some NOS and you are good if you wanna drag.
I am sure that you are aware you have to put alot of new parts in your 88 when u do this swap....mounts, engine harness, axles, tranny, dizzy and some other stuff.
I havent heard of a B16 head on a B20..the former is a VTEC head...isnt it?
Its alot of work but if done right...you will have a great car.