Aight, Well I haven't heard of a B20 bottom and a H22 Head, for a 3rd gen I have seen and H23 bottom and a H22 Head, that swap is straight up, I havent heard of swapping the whole H22 engine into a 3rd gen. but anythings possible, from my knowledge this is what you will need.

1.) New Tranny, either H23 or H22
2.) New Engine, either H23 or H22, either whole H22 or H23 bottom-H22 Head(good luck on finding an H23 in the first place)
3.) New CV joints
4.) Appropriate ECU and wiring harness
5.) Then weld and cut to get all that shit to fit in a 3rd gen.

Don't know anything about B18 you might want to try the Civic or Integra forums.
Good Luck