B17A, B18B1: The B17A could be found on the 92-93 GSR producing 160hp @ 7600 rpm and 117 lb.-ft @ 7000 rpm. The B18B1 is the later model Integra LS, RS, and GS engines. They don't offer huge power outputs at 142hp @ 6300 rpm and 127 lb.-ft @ 5200 rpm, But they can be had for very cheap as they are plentiful and not really sought after by many people. The exception being for the B17A as it did have greater power output but they can still be had for cheap as they are generally older and in worse shape compared to the newer B18’s. Anyone of these should still offer a cheap, reliable power upgrade for your small civic. Anyone of these engines could be found for under $2000. The downside to these cheaper engines is their Rod to Stroke ratio. The B17 isn’t that bad but the B18B1 has a R/S ratio of 1.54. This does considerably reduce the maximum possible power output from these engines. But if you don't plan on turbocharging this engine past 15 psi or letting it rev to 11,000 rpm, then it should meet your modest power needs.
B18C1: Probably the most highly sought after swap candidate, this powerful little engine came on the late model Integra GSR and produced a hefty 170hp @ 7600 rpm and 128lbs-ft @ 6200 rpm. It is rather expensive at around $3000-$3500 and they are a little on the rare side considering everyone wants one, but a simple swap and your pocket rocket will be pushing high 14's with a stock engine. Even more by adding the small bolt-ons. And greddy has a bolt on intercooled turbocharger kit that'll give around 240 wheel hp. Which should put you deep into the 13 second range, possibly high 12's. This is the most desired swap candidate.
B18C5: This naturally aspirated wonder came on the late model Integra Type R and produced an even greater 195 hp @ 8100 rpm and about 130 lb.-ft of torque @ 7500 rpm. This is even more highly sought after than the GSR engine. And would in fact be more popular if it wasn't for its $5000+ price tag. But if you could afford it, there are few engines that would be as painless and give you the fastest performance available for the civic. This regarded as the naturally aspirated wonder because it does well producing large amounts of power without the need for snailshell's. Although a turbocharger can be bolted on to this bad-boy, it's generally not recommended, as this is a very high compression engine. If you were to used forced induction on such a high compression engine, you would either have to build it accordingly, have a REALLY good engine management system ($$$) or watch it blow up on the first run. The C1 is better suited for forced induction and would cost less in the long run.
B20B, B20Z: The B20 engine is the newcomer in the game and is highly acclaimed by its supporters. It has several key characteristics that give this engine real potential no matter what route you decide to pursue. The B20B came on the 1996-1998 CRV and the B20Z came on 1999-2000 CRV. The B20B made 126 hp but the real jewel was the 133lbs of torque that was easily achieved almost anywhere in the RPM band. It is a small displacement engine that has flat torque line!!! Additionally it was a comparatively low compression engine which means that turbocharging to decent levels is possible without the need to spend hundreds on rods or pistons. The B20Z was more or less the same as the B20B but they changed several head characteristics and the compression was bumped up to increase the horsepower to 146.