Don't know your age
but if you're under 21, you'll have a 2-year 33bhp restriction.
As for the GSXR600 / R6 for starting out, I'd advise against it as well because
a) insurance will be sky-high (assuming you can get it),
you'll almost certainly drop it at some point, and a faired bike will make you cry with the cost of putting it right (replacing the damaged plastics is expensive).
c) high pegs and low bars can get to be bloody uncomfortable over distance.
d) high-performance bikes like the GSXR / R6 frequently to get a hard life; they may often be "low-mileage", but there's a good chance that it'll have been hammered for those miles. In addition, they may well have done there fair share of wheelies etc which can be hard on forks, head bearings, chains and sprockets. £2k / £2.5k is unlikely to get you the cream of the crop here.
e) these bikes tend to be highly strung, and any slight error can have the machine tying itself in a knot that you can't get out of.
Have a look at those bikes that MM suggests, also the Honda CB500 or Kawasaki ER5 / 6 (your budget should get you an early ER6 if you look; my local bike shop had an 07 plate ER6n at £3k, if you pay cash and / or haggle, you'd probably get it for £2500-£2700).
Hope that helps.