If you are serious about having a track car then, IMHO, your first mods should be suspension related. An LSD literally transforms the car, if you don't want to spend that sort of money then you're not really making a track car you're just driving a stock/stripped/fiddled car on a track.
For the rear axle I would suggest getting a subframe and refurbing it (strip/protect/paint) along with poly bushing it all, then just swap them over.