As many others have noted, it would help to know what type of long range shooting matches you're talking about. If we're talking about amateur DM courses where you're just trying to ring 10" gongs between 300 and 600 yards, you don't need anything fancy.
If you are new to the long distance world there are a lot of things to look at. Do you reload? If you don't reload then you will definitely want to choose a caliber that is readily found at a reasonable price. The inherent accuracy that 6mm ppc and 6.5 rounds are capable of really won't matter as much when you're just learning to shoot at 500+ yards, especially when you need to put rounds down range for practice and good ammo in these calibers will cost twice as much as decent practice .308 ammo. For this reason, I recommend you start with a common caliber. If you reload it's not as big of an issue, but even then a common caliber still has it's benefits.
I also espouse the same beliefs in frugality about a rifle. Many may chime in or disagree, however a Savage rifle is kind of hard to beat. They're relatively inexpensive and almost always 1moa accurate right of the box with the right ammo. This is good enough to learn on and a Savage is not hard to upgrade. An amateur, who is careful, pays attention to detail, and is somewhat mechanicaly inclined can do a barrel/caliber change. Soo... if you get good and want a more inherently accurate round than .308 then you can change calibers. As for glass... if you're limited on money then I would stick to a fixed power scope with target turrets and really good glass. I cut my teeth on a 10x fixed Bushnell Elite 3200 that I bought for 200 bucks. While I would advise starting off with a little better glass than that if you're trying to shoot at 1000 yards, it'll do. You don't have to drop 5k to get started long range shooting, or even competing (on the amateur level, of course). You can get started on a shoestring budget, but what you buy now can save you money in the future (the ability to change barrels and work on the Savage means you'll get more service out of it as opposed to having to buy another rifle later).