Wow, I didnt think id find a honda guy on this site.
YOu are in luck, I have built and do build honda stuff for my other project. (91 honda Civic Hatch.. mainly being built for road raceing) I am currently building a 1.8LS for my hatch.
IN short.. what you have there is one of hondas best motors as far as power and torque go. You can get alot out of that motor if you really want to. just remember that the farther away from stock you go, you will trade off reliability and you will need to make sure that it is tuned correctly or you could have problems.
I will assume that you have the LS version (non Vetc) which is about a 145hp 130tq motor stock, pretty respectable. that being said, you can swap the head off of a B16 Vtec which will bump up the compression ratio and the head has good flow. I dont have any dyno sheets but this should get you close to 200HP and still be reliable basically a stock set up. this set up is very popular and easy to do (search LS-Vtec or even better Frankenstein) on a site like Honda Swap or Honda Tech (see links below) and you will find all of the info you could ever want. Oh, and for the money, a typeR is not going to gain youmuch overy what you have fr the money... there are more effective ways to go and get solid power out of the motor without doing anything that intensive.
My build will be a 1.8 bored out to be a 1.9 Fully forged bottom end (crank, rods, pistons) ported and polished heads (using stock LS heads) 2.5" custom exhaust, Intake , a bit hotter cam than stock and an Apexi SAFC-II and a few other goodies. all said and done it will be a solid 200hp motor with room to improve. It will be trubo ready should i ever want to go down that road.
Right now, i have the machine work done and the parts, just need some rod bolts and a few other things and i can start to assemble it.
Let me know if you have any specific goals, or what your budget is and i can point you in the right direction... also your elvel of experience and what you or anyone helping you is comfortable doing... and I wouldnt go with a turbo unless you have alot of cash and tuning experience or things can go BOOM easily and you can kiss your $3-7K good bye.
Oh, you said you want to keep up with your buddies 300zx, does he have the standard version or is it a twin turbo set up... this will help to diagnose how to beat him in a foot race

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Here are a couple sites that you can look at for alot of good info.
http://hondaswap.com/
http://www.honda-tech.com/index.php