I wouldn't buy a dated r6 for that kind of money. Prices are lower now (winter) and there's way better options, just don't jump on the first thing you see and be patient.
Here's a list of bikes I've picked up in the last 2 years in your price range or lower:
06 triumph Daytona 675 for $3300 (no issues, never dropped)
08 Yamaha r6 Canada edition for $4000 (needed tires, never dropped)
04 cbr 600rr heavily modded for $2700 (needed nothing)
04 ninja zx6r for $1100 (needed $300 worth of oem parts which I installed and a rear tire)
07 ninja zx6r for 3400 (needed nothing)
I'm all for learning on a 250 but IMO it takes about a month to out grow one.