Step Zero is always to RTFR--Read The Rulebook.
In some instances, engine swaps can add the requirement that you use a lot more safety equipment than you might otherwise need. While more safety equipment isn't bad, it can be a pain to live with in day to day driving.
Usually engine swaps will put you into classes where you will need to do an awful lot to the car in order to be even close to competitive.
If you're not willing to do a crap-ton of suspension work, adding lightness, roll cage fab, and so on, it may be best to stick to the stock engine.
Besides, you have have an awful lot of fun in a basically stock CRX...
"Mango Bango", 1990 CRX Si -- Sold on 10/01/11, with over 227,000 miles.
VTEC is Honda's "select a cam profile on the fly" system; VTECH is a crappy phone.