First question: 1st-gen (83=87) or 2nd-gen (88-91) CRX? They're quite different, and the differences have a significant effect on the "easy" swaps.
Most 1st-gen CRXes are carbureted. Only the Si models have fuel injection. This makes a big difference because the fuel supply is different on the carb'ed cars, and it is more complex to make them compatible with fuel injection.
The "DX" (or "standard") 2nd-gen CRX had DPFI, Dual-Point Fuel Injection. It had two injectors pretty much at the throttle body. The wiring is pretty different from the MPFI (Multi-Point Fuel Injection) that the HF and Si models had. (An MPFI swap is a popular mod for DX cars, by the way.) Pretty much every engine you might want to swap in will be MPFI, as well.
Assuming you have a 2nd-gen CRX: The transmission you want is the HF version. It has the tallest gears and also the tallest ring and pinion ratio. So the engine will be turning fairly low revs on the freeway. However, this transmission will only work with D-series engines. If you're looking to swap in a B-series mill, you'll need a B-series transmission.
The regular HF motor would be the easiest one that gets excellent MPG. It should be a bolt-in operation, except for the possible MPFI conversion. Other D-series possibilities are... Well, just about anything frankly. Most D-series engines are 1.5 or 1.6 liters. Some, such as the D16A6 (88-91 Si) and the DOHC ZC (a Japan-only motor that is a popular import for swaps) are designed more with top-end power in mind, so they aren't as good on economy, but none of them should be awful.
There are later D-series VTEC equipped motors. A few, like the one from the Civic VX, are optimized for economy. Some are optimized for power. Many are somewhere in the middle.
A reasonable forum for CRXes in particular can be found at
CRX Community Forum • Index page . It's less active than honda-tech, but you'll find less locker-room language and less overt stupidity there as well. (Though H-T can be worth sifting through the crap because there are some really knowledgeable people over there too!)
Check into your smog laws. I know that, in theory, a swapped car must meet the smog requirements of the later of the engine or chassis. So if you put a 1996+ engine in, it has to have all of the OBD-2 equipment on it. And theoretically, non-US engines cannot be used, nor can truck engines be used in cars. Practice may be different than theory, though.
-soD
