The fastest-spooling turbo on your car would probably be a ball-bearing T3 unit -- but what you're missing is that spool time and overall power are generally a tradeoff.
I could give you a turbo that would fully spool by 1800 RPM's, but the only problem is the boost would drop off to nothing by around 5K RPM's. You'd have lots of power right off the line, but you'd have nothing after you rev it higher.
When you're racing, you don't "start" at 1000 RPm's -- you likely do a little baby launch at around 3K or higher. So if your turbo doesn't start to spool until 3500 RPM's, it really doesn't matter because you're likely gonna start there anyway.
Think about it this way too -- if your turbo is perfectly happy to spool at 2K RPM's, then driving down the highway at 75+ mph is going to be a nightmare. Fuel mileage will go to hell, driveability up hills will get "surgy" if it's not tuned exactly, et al. Just ask Random about his "too eager to spool" Alpine kit.
A "larger" T3 turbo would spool relatively fast (start making positive pressure probably around 2800 RPM's) but would be able to HOLD that boost until redline.
Other things that influence spool time: load on the engine, compression of the engine, cams, fuel tuning, ignition timing (yup), manifold tuning (log style = very bad flow) and air temperature (you'd be suprised)
-Red-
