First off welcome to HAN.
Now for your questions: Yes an Integra is a great car for some speed, handling and reliability. It also looks great as well.
1. Will a '94-'95 or so year model Integra (GSR , RS, or LS) be as reliable as I'm thinking it will be?
Yes it will be. They are very reliable when taken care of.
2. Can I get a decent one around that year for $5k if I want a 5-speed and A/C as the only requirements?
Yes you can definetly get a 94-95 ls or rs for that price and if your lucky enough you can get a GSR for that price. They all come with a/c. Just look around for a 5-speed. GSR's only come in 5-speed but ls and rs come in either 5-speed of auto.
3. How much more hp can I get out of the RS/LS engine with intake/headers/exhaust/ECU? How much out of the GS-R?
This depends on what setup you have. Most I have seen out of a GSR is 20whp with a comptech i/h/e setup.
And don't alpologize for being a newbie. We were all once newbies. You aksed good questions. Let us know how your search goes. :thumbup: