The 92-00 Civic and 94-01 Integra share a very similar chassis and can fit almost any of their engine choices into any of the models of each car, as well as some other engines. Because most people won't want to swap their Civic CX's high output powerplant into an Integra TypeR, we'll stick to engines that fit and improve performance with as little modification as possible.
B16A3
Donor Car: 1994 & 1995 delSol VTEC
Specs: 1.6L, Inline-4, DOHC VTEC, 160hp & 111lbft of torque, 8000rpm redline, OBD-I wiring, hydraulic 5spd transmission.
Price: Since the A3's are fairly difficult to locate, their price sits in the higher $2,000 range. Last I had seen was $2800. As always, check eBay if you are horribly strapped for cash. You can also contact HondaMotorsOnline or Inline Four for their abilities to get you one.
B17A
Donor Car: 1992 & 1993 Acura Integra GS-R
Specs: 1.7L, Inline-4, DOHC VTEC, 160hp & 117lbft of torque, 8000rpm redline, OBD-I wiring, cable 5spd transmission.
Price: B17As are pretty hard to find because they are available in extremely limited qualtities. However, they sell faily cheap, in the low $2000 dollar range. I have seen some go for $2000-flat for the full swap. You will have to get an adapter for the cable to hydro conversion.. or you can just get a hydro Bseries transmission. Keep in mind that there can be legal problems if you swap this engine into a 1994+ car because the B17 was only available in 1992 and 1993 and the year of the engine must be later or equal to the year of the car. For best luck, contact HondaMotorsOnline.
B18B OBD-I
Donor Car: 1994 & 1995 Acura Integra LS/RS/GS
Specs: 1.8L, Inline-4, DOHC, 142hp & 125lbft of torque, 6500rpm redline, OBD-I wiring, hydraulic 5spd transmission or 4 speed automatic.
Price: Full LS swaps are selling for a very nice $1500 or so at many online and local engine places. Finding an OBD-I isn't the issue that it is for the VTEC engines.
B18C1 OBD-I
Donor Car: 1994 & 1995 Acura Integra GS-R
Specs: 1.8L, Inline-4, DOHC VTEC, 170hp & 128lbft of torque, 8000rpm redline, OBD-I wiring, hydraulic 5spd transmission.
Price: OBD-I GS-R engines are fairly rare because many have high milage and are still in their original cars. I ran across one for about $3000 on eBay, but I haven't seen any since.
B16A2
Donor Car(s): 1996 & 1997 delSol VTEC (for 1996-1998) & 1999-2000 Civic Si's (for 1999-2000)
Specs: 1.6L, Inline-4, DOHC VTEC, 160hp & 111lbft of torque, 8000rpm redline, OBD-II v1 wiring (from the delSol) OBD-II v2 wiring (from the Si), hydraulic 5spd transmission.
Price: As one of the hottest swaps for its price and efficiency they sell for a bit over $2000, up to $2500. Anything more than that and you aren't looking hard enough. They are more available than you are on a Friday night.
B16B
Donor Car: 1996-2000 Honda Civic TypeR
Specs: 1.6L, Inline-4, DOHC VTEC, 185hp & 117lbft of torque, 8500rpm redline, OBD-II wiring, hydraulic 5spd transmission.
Price: The ultra rare B16B swap can be had for about $4000. However it is very unpopular because for $2000 less you can get a B16A2 and put $2000 into it to match the B16B's price. This engine is either for the dumb person with lots of money or the ultimate JDM whore.
B18B OBD-II
Donor Car: 1996-2001 Acura Integra LS/GS/RS/SE
Specs: 1.8L, Inline-4, DOHC, 140hp & 125lbft of torque, 6500rpm redline, OBD-II wiring, hydraulic 5spd transmission or 4 speed automatic.
Price: Full LS swaps are selling for a very nice $1500 or so at many online and local engine places. OBD-II's are in good supply.
B18C1 OBD-II
Donor Car(s): 1996-1998 Acura Integra GS-R (for 1996-1998) 1999-2001 GSR (for 1999-2000)
Specs: 1.8L, Inline-4, DOHC VTEC, 170hp & 128lbft of torque, 8000rpm redline, OBD-II v1 wiring (from 96-98) OBD-II v2 wiring (from the 99-01), hydraulic 5spd transmission.
Price: OBD2 B18C1's sell for about $500 more than B16A2's. Usually they can be found a few hundred dollars north of $3000 for a full swap. They are also readily available and very popular.
B18C5
Donor Car: 1997-1998 Integra TypeR (for 1996-1998) & 2000-2001 Integra TypeR (for 1999-2000)
Specs: 1.8L, Inline-4, DOHC VTEC, 195hp & 130lbft of torque, 8500rpm redline, OBD-II v1 wiring (from 96-98) OBD-II v2 wiring (from the 00-01), hydraulic 5spd transmission.
Price: The B18C5 runs upwards of $5000. Honda Motors Online has them for $4700. They are semi-limited and are the choice of someone with a lot of cash and a need to have the top-notch Bseries.
B20
Donor Car: 1997-1998 CR-V (B20B) 1999-2001 CR-V (B20Z)
Specs: 2.0L, Inline-4, DOHC, 126hp (B20B) or 146hp (B20Z) & 133lbft of torque, 6000rpm redline, OBD-II wiring, transmission must be used from a B16 or B18 engine.
Price: Because the transmission doesnt come with the swap, the B20 longblocks both sell for around $800. It is one of the most solid swaps for the dollar of any of the Bseries swaps. They also have great potential for boost or adding VTEC to them.