I agree with RSixxy. The yzf600r is quite a bit heavier than some of the other contenders. For the same price you would do better off getting something else. I liked your idea about an F3, and it is right around your price range.
No, and if you do insure it (no reason to if it is track use only), don't ever claim the damage. It won't be covered. Same goes for taking a street bike to a track day. You drop it or get knocked down? Oh well. If you get taken out, the other rider's responsibility begin and ends with "Sorry.".
As to bike choice, it all depends on the type of track riding you want to do. Are you looking to get into a competitive class? If so, SV650 for the lightweight twins or any of the current crop of inline fours for the supersport/superbike classes. Be prepared to spend serious coin in doing it.
Clubman classes are cheaper and fun. GS500, Ninja 250/500, etc. Many orgs have a novice/clubman group. Just as fun to drag a knee on a Ninja 250 as it is on a 600. Probably more so since rider skill plays a b***** part in the smaller displacements.
The GP bikes are fun too but costly to maintain. If I could afford an 125cc or 250cc GP bike, I'd run that. No torque but wicked corner speeds.
If you're just looking to have some fun, consider Vintage. Many of the older crop of sportbikes are classed as vintage heavyweights. Smaller grids and a more mellow type of racer for the most part. I'm prepping an FZR600 for WERA Vintage V6. I could run it in the novice superbike classes but I'd be lapped. Plus, I'd rather share the track with 20 other racers in a mixed class than 50 novices on their supersports. I don't have the raging competitive spirit anymore and I am just looking to do track days and push my own limits. If my times improve and I'm not the last one across the line, I'm happy.
Tons of options out there. I ride an FZR600 on the street so that helped narrow my track choice. If I wreck the FZR on the track, no great loss. I building the bike from the bolts up and I can use the parts that survive as spares for my street bike.
Not that my 250 is considered a true GP bike, but running costs aren't too high for me, and I stick right with the big boys, even passing some in the corners, and I'm not THAT good yet, although I am getting alot better with each track day. Aprilia RS250's are just awesome, a great way to start if you want to get to a true 250GP bike eventually (Aprilia RSV250 for me if I can find one) you've also got the Honda NSR and RS250R, along with the Yamaha TZ250, all awesome bikes, and at most tracks you go to many of the top lap times will be held by 250's. You can find a TZ250 for about $4500 with a nice spares package too, great power, lightweight, and just a ton of fun to race (even for us taller riders!)
But if you want a basic low maintenance track bike, get a Suzuki SV650S like everyone else has been saying. But remember with the SV650 it takes a little suspension work to get it happy on the track.
I know of the sv650, and when I mean track bike, i mean track only bike. I ride my duc on the streets. I want more hp on the track though, My duc would be too expensive for me to replace parts if I wipe out, and it's in prestine condition. My cousin and uncle race on the track on their R6 & gxr 750. I love curvies and after five yrs of riding the road, want to really push curves, and I figure best place is on the track, and I would like to race with my cousin and uncle. sv650 i know is a great track bike, but to me seems under powered on the straights of the track. But I love twins and if I had the money would get a big liter twin (duc 999, mille, TLR, RC51 etc), but i don't have the funds, soo I have to sacrifice the twin idea for more hp or less power and settle for a twin. I choose the hp to push on the track.
in the pics
1st pic: my cousin on the blue r6
2nd pic: my uncle passing on the outside on his gixxer 750
I get first hand view of what torque can do when coming out of the corners on the track. As I'm revving the hell out of my Honda in 2nd gear, the V-twins are in 3rd or 4rth gear and doing it with much less risk or drama. Because of their torque advantage, I have to be harder on the brakes and more aggressive with corner entry speed to get around them. It isn't easy to try and pass on the power. :leghump