Very nice! I have an 88 LX sedan. No B engine in it though.
For the transmission, you'll have to find a cable clutch B series transmission. The only choices in the US are the B16 and B18 transmissions from the DA Integras. You can find a few JDM transmissions lying around also, but they're getting harder and harder to find. Hydraulic clutch transmissions (94+ Integra, del Sol VTEC, 99-00 Si) are all over the place, and you can get conversion kits to make them work in your car.
You'll also need a swap mount kit to put the B engine into your car.
If you want to skip the B transmission, you can try to use a B to D conversion kit. There are a few out there now, and they basically convert your D series transmission to work with your B series engine. This makes a TON of things easier- mounts, shift linkages, clutch actuation, etc.
Electronics- you'll have to convert to MPFI if you aren't already. The straight B20 doesn't have VTEC, so converting the car to run on the Si PM6 ECU with a chip socket will work. Hondata isn't necessary- there are quite a few DIY alternatives for the non-OBD car. As far as harness, it does matter- Hondata uses the stock ECU, so you need to be wired to take whatever ECU your Hondata setup (or other tuning solution) is going to live in.