Hey man... I would suggest the H22A over the K20A...
The K20A has better gearing, which makes it quicker... but its a lot more expensive.
The H22A will give you 13's no problem. If you are serious about doing the H22A I've got almost everything to make it super simple for you.
I'm trying to sell hasport mounts, gator axles, lsd tranny, perfect head... everything but a block. It's all for an EG, so you are in luck haha. I've even get the wiring harness to sell you so you can just make it plug and play. Let me know if you are interested. I can save you a ton of money and time.
H22A-Civic-Integra-Parts-Mounts-Axles-Head-M2B4 Tranny-More