If you want an Integra, either way you go is a good investment! My cousin has a '94 LS and has almost 200K miles on it. I have a '98 GSR and have over 100K miles. Our cars still run well. Both our cars are 5-speeds (GSR only come with 5-speed), both are 4-door sedans. I recommend that if you are getting an Integra, go with the 4-door, since you will be going places with friends, so it is more comfortable, and insurance is cheaper on a 4-door than a 2-door hatch. (the hatch is faster in the 1/4 by approx .2 seconds both have same mph)
My personal opinion is that the GSR is more fun to drive, just because after 5500 rpms it takes off in every gear including 5th!!! That is stock!! It also handles better through the corners. However, if you live where there are not any fun twisties to drive on, and you will be sitting in traffic all day, the LS is the better deal.
The gas mileage is about the same, my best run was from Columbus, OH to Tampa, FL (around 1,000 miles) in 12hrs and 45 minutes including stops for gas and restrooms, while averaging 35mpg!!!!!! If anyone can beat that please let me Know.
With the gas prices rising, a 13.2 gallon tank that can take you over 350 miles per tank in the city with the A/C cranking, is a friend to the wallet! However with the 10:1 compression in the GSR, prepare for 90+ octane vs 87 in LS.
Good luck with your search, I know 4 doors are very hard to find and more expensive, but parts switch out with hatches except exhaust - 4 door is longer, so stick with your budget and you can't go wrong with an Integra!!