Prefer 308 and I said between. 500-800 maybe more.. will be doing local distance competitions and just a fun gun to take to the range 500yards..
Sorry, I misread the distance.
If you are doing competition read the rules first. Some (like F-Class/TR) specify the calibers you have to use.
I would still steer you toward the .260 or even the 7mm-08 over the .308, especially if you hand load.
I have a Savage 110FP in .308 with a 24" barrel (pre accu-trigger) that will shoot almost anything I put in it sub-MOA. Even "surplus" 7.62 NATO ammo goes ~1 MOA. Regardless of the cartridge you shoose, it's just hard to go wrong with a Savage in your price range.
Speaking of your price range...
For about $1000 you can buy a donor Savage Model 11 in .243, 7mm-08, or .308 (a new model 11 will run ~$450-$500) and send it to McGowen and it will come back with a custom barrel made and installed to your specifications for ~$300. Put on an aftermarket stock to your liking for a rifle that will likely outshoot you. Or just shoot it the way it is for a while and then spend the money on a barrel and stock later when you eventually decide what you really want/need.
If you really want to get fancy you can buy just a Savage target action, which will give you a very nice target trigger (it will help
a lot at long range). Check out "Northland" at the savageshooters.com forum.
http://savageshooters.com/SavageForum/index.php/topic,7912.0.html
I bought brand new Savage 11FCNS and had a McGowen barrel put on for ~$750, but I kept the factory stock (it's a hunting rifle). My hunting load shot a 0.4" 3-shot group a few weeks ago. My largest group while working up loads with various bullets and powders was 1.2".
Now that I have had a custom rifle barrel, I don't know if I can ever buy a factory rifle again.