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I highly recommend that you try the 3 types. If you do, I'm pretty sur you will be disappointed by the LS. It really lacks power.
The GSR is really better. It feels more like a sport car.
The Type R is a completly different beast. I've tried some and it's really a great car. The only drawback it has is the tires. It would deserves 17'' tires.
Choose the one you want, but like I said, I strongly suggest that you make sure you've tried the LS properly so that you feel disappointed for years after.
Another idea is to buy a LS for now, and when money allows, put a Type R engine in it. You will have the luxury of the LS- sunroof, A/C -, and Type R like perfomance. Even better, there are a lot of modified cars on sale. I'm sure you can find an LS with 17'' pretty easily. Begin with that and put a type R engine later. Changing the engine is expensive, but you will have a new engine.