I shoot conventioal (sling), but shoot with the F-Class guys, so my comments are what I see used and winning at matches in the F-class classification.
I agree with Jim on about everything he says. If you are on a buget, I don't see anything better than the Savage set up for F/TR. The Team Savage took box stock rifles, and are winning or placing real high here and around the world. They have posted anwers to questions on after market gunsmithing, and they say they didn't need any.
F-Class mathes start at Mid-Range which is 600 yards, you could get by with a .223 real easy, but wouldn't be the best choice for the 1000 yard matches. The only choice over all would be the .308, unless you want to go open class.
Another option is to pick up a used rifle, there are always rifles for sale. Some guys are always looking for the "magic rifle" and trade often. I bought almost all my competition rifles that way. I also have a Savage that I'm real impressed with.