Honestly for long range shooting I'd be looking to spend at least $12-1300 on a scope if not more, not including the rifle. That said, I hate to direct you away from this site, but I'd head on over to snipershide.com. You will generally get much more and better information when it comes to long range tactical shooting.
That said, if I was on your budget and I was trying to get a decent set up, I'd look at one of the Savage 10's or 11's. There are several variations and while most of them are extremely accurate, If I didn't plan to re-barrel it, I'd be tempted to get a heavy barreled one from the get go.
For the scope, imo for the $500 range there are really only a couple of good options. For long range shooting you need a scope that is repeatable and that you can crank on the turrets and be assured it can track correctly. Most cheaper scopes have an issue with this, and while they work fine to dial them in and then hunt with it, never touching hte adjustments again, they don't work for long range shooting.
The SWFA fixed power scopes can be had in your price range and are a decent choice. There is also the SWFA SS 3-9x42 that can be had for $100 more than your budget. I honestly like more than 9x power on the top end for 600 yards plus, but you can get by with it.
The Weaver Tactical Midway exclusive is also getting pretty decent reviews.
There is also the Bushnell Elite 10x fixed power scope that is decent, but having had one, it's no where near the quality of the SWFA scopes. You can get one of these for $200. The one I had tracked well, but that was about the only thing I liked about it. For $200 though it would be good enough to get you by for a bit while you saved up more for a nicer scope.
Now that said, while I think you can get by with that rifle and that scope, I'd be inclined to start looking at better glass. The Vortex Viper PST's seem to be decent if you are on a budget and the SWFA 5-20x50 is a good scope on a budget as well. However, they will spend almost your entire budget on a scope. Then you have Nightforce as the next step up, which are great scopes. Then from there you have USO, S&B, Premier, and a few other brands, which while nice a Nightforce or SWFA scope will probably do everything you'd ask of it.
I think the rifle is a good choice no matter your budget. Once you start spending more, you can start getting a custom rifle, but I really don't see the need for that unless you are trying to get the most accuracy out of it.
As for the caliber, there are really a ton of great choices out there and it all depends on what you really want. The 30-06 is one of my favorites even though .308 seems to be a more popular round for tactical shooting. Both are excellent choices. The 6.5 Creedmoor is also a newer cartridge that is getting a ton of great press. There is also the 260 that's a good choice as well. Really there are just a ton of great cartridges and you just need to pick one that meets your needs. I tend to shy away from the Magnums, but that doesn't mean they are bad. Some guys like them as well.