I'll echo what has been said before - if you live in a state that gives a shit about swaps/emissions, you'd best be careful.
With that out of the way, there are several ways to do this, with varying expenses/difficulty levels. You have two basic choices: 1. Keep the car OBD2, convert the motor to OBD2. 2. Keep the motor OBD1, convert the car to OBD1
In order to convert the motor to OBD2, the main PITA thing you will have to do is install the crank fluctuation sensor from a 96+ LS motor. I am not sure if this is a trivial task on a B18A1 - I've only ever removed them from OBD2 motors when going into OBD1/0 cars. Aside from that, you're going to have to repin the distributor. I'd recomment taking the plugs off your old DX distributor and swapping wires - unpin both the OBD1 distributor connector and your 98 DX distributor connector, move the OBD1 wires to the 98 plug. Once that is done, grab a 96-98 LS ECU and hope for the best. You might have to lengthen/relocate some wires (thermoswitch for fan, etc.) but USE THE 98 DX HARNESS!@!@!@!
The other (and better) option is to use a 92-95 LS ECU (which you might already have, considering you have a 93 motor) coupled with an OBD2A-OBD1 conversion harness. Additionally, the same advice as above about repinning the distributor and moving wires applies. You do not need to install the crank fluctuation sensor tho. Keeping the motor OBD1 and using an OBD1 ECU will make it much easier for you to chip the ECU or run a hondata in the future.
peace
-Dave