Yes a GSR would be a better platform than the LS for anything (Turbo, Nitrous, All-Motor, etc.) but you won't find a 3rd gen one (94 and up, you're looking at 96ish) for only 4 grand. The GSR and non-turbo Eclipse aren't even in the same ballpark...

An early 3rd gen Integra LS/GS/RS (for 4 grand, that means a 94 or 95), is perfect for that pricerange. Very reliable, pretty quick (about a half second faster than an Eclipse stock). And there are tons of possiblities you can do with 4 grand in your pocket. You can easily have a 13 second daily driver

Good luck!