Other than the fact the B18c motor is a great little motor, are there any other reasons it has to be a GSR?
You have quite a few possibilites should you go with the GS, not to mention cheaper insurance.
You could do an LS-Vtec conversion. These can be done PROPERLY, and SAFELY nowadays without breaking the bank... if you're paitent you might even be able to find a nice, low km B18c5 motor/tranny for a good price. You could also do a custom turbo kit on the B18b motor...
Or if you really want to go crazy, you could save your pennies for a K swap.
Parts are all over the place for the Integra. I think it's more important to find a good shell, free of accidents and rust. If that GS is a colour you like that's another added bonus.
Don't be too quick to dismiss it. This is just something to think about.
If you do decide to go with a GSR, just be paitent, and the right one will come along in due time