Everyone always says to put a K series in the civics
According to the Zealworks Transmission calculator, it looks like the H22a tranny is comparable to a GSR tranny, and a bit shorter geared than opposed to the LS tranny. The B16 tranny seems to be the shortest geared out of the bunch but there's a lot of different B series trannies, and if you do the H2B then you always have the option to run a F-series transmission seeing how they're interchangeable between the F and H.
So the question is... do you want shorter gears or longer ones? And can you afford the 800$ for the H2B conversion kit?
About the motor mounts, if your putting the H22 into an EK shell, then your going to need H22 EK Mounts, which you can get here:
http://www.swapshopracing.com/contents/en-us/d676.html

If you'd like to take a peek for youself, here is a link to the calculator below:
Honda Transmission Calculator by ZealAutowerks

Hope this helps you out.