Yeah, pretty much.

You have a few options, but any of the B-series motors you listed will fit just fine with a mount kit and the right transmission. Your civic has a cable that connects the clutch pedal to the transmission, all '94+ Integra transmissions will use a hydrolic system. A pre '94 Integra transmission will work just fine but will be longer geared than the GS-R tranny. There are first gen JDM B16A transmissions that you can use as well. The H22A is a little more complicated and I don't know if anybody makes a bolt in kit for EF civic's (probably, I've never looked for one).

To determine what's right for you, you need to take a step back and decide what you want from the car. Straight line speed, fun daily driver, track car ... and pick the motor that best fits that need.

Be careful over there.