Well 3k for upgrades seems low if you want to perform better than a GTS, with $4k (turbo kit) you can have your GT 140 HPs to 210 HPs, which is not worth at all because you have 180 HPs on the GTS stock + 6 speed transmission instead of 5.
But, if you want to virtually do this to see the performance comparison you can do it with a car performance simulator, there you can race a GTs vs a GT with the mods you choose and so on, you can eve set up your weight as driver for real life results.
Try it at
http://www.nxgtrsim.com