Q&A

 Master

I assume your car has multi port fuel injection (the CRX had 3 engine options that year one was throttle body injection the other two engines have 4 fuel injectors). You are starting off on the right path by tuning the car up seeing as you just bought the car and do not know the previous service history of the car.
The throttle body cars had some injector problems (seats pounded out in the injectors mostly causing high emissions) the port fuel injected cars didn't give much problems if someone changed the fuel injectors occasionally and didn't drive around without the gas cap fitted.
Did you adjust the valves? Important on a Honda (leave them a little loose rather than going for the minimum spec), then check the compression using a compression gauge to ensure the compression is even. Were the spark plugs all about the same color and condition (none damaged or oil fouled)?
Next check for vacuum leaks around the intake manifold or hoses.
If all these are OK you need to check fuel pressure and fuel delivery volume (about 1 pint in 10 seconds).
I have seen cars come into us with low intake manifold vacuum, drivability problems were the timing belt was installed one tooth off, but I hope your problem is more basic than that (Check the valve timing when you have the valve cover off to adjust the valves its easy).
Visually check the ignition system especially the rotor and ignition coil.

I had VERY similar problem. Take your catalytic converter off and shake it. If anything rattles, replace it. Mine was bad and I changed it with a cheap Ebay one($25.50 shipped) and bolted it on it ran perfect. Mine CRX Si was only allowing it to idle and if I gave it anygas it bogged MAJOR. Let off the gas and it would idle great. Just unbolt it and shake it. Takes a few minutes but will tell alot about if thats the problem or not. Could be contributing. Matt