If you don't have the ability to do the work yourself, budget a MINIMUM of 20K. If you do have the ability to do it yourself, you will need a basic budget of 10K (That's just buying stuff, and fabbing it...)
I'm halfway through putting an LS1 into my R33. It doesn't leave you with more room, in fact, you end up with less. The motor is the exact same length as an RB26 (I had both sitting side by side) and is MUCH wider. You also need to factor in getting a 2.5" exhaust pipe down past the steering column.
You will need custom mounts, custom tail shaft, to fabricate up clutch lines, all intake to be custom, radiator lines modified etc etc.
Basically EVERYTHING needs to be custom.
It is NOT a simple conversion, although you really don't have to cut much, just that everything needs to be custom made.
Engine is lighter, but the gearbox is heavier, you end up winning by around 20 to 50KG at max.
Edit: I'm also making things easier and ditching all emmisions gear as this is going to be track only.