If you're looking for out-of-the-box accuracy, your best bet for your money would probably be a savage that comes with the accustock and accutrigger. the 111 LRH models have a good reputation. But really, any savage with those factory upgrades will do. As for a scope to go with it, if you buy a combo, ditch the scope. I need to ditch my factory scope for sure. Nikon makes some of the best for the money. with out a doubt, you can't go wrong with Nikon.
Savage is a great out of the box rifle. Next, I would look at the Remington 700 Sendero, Tactical or Varmit if you want to step up a little in price. From my experience, these have all shot very well. Just my 2's worth.
Look for any of the factory offerings that come with a muzzle break. Then you can shoot the heavier calibers with ease and not turn your shoulder to hamburger. To 500yds, 308, 7mm-08, 260, 6.5 Creedmoor, 25-06, 30-06, 284 Win, 280 Rem, 280AI would be the ones I would look for in standard calibers. If you want to go magnum, then anything 6.5mm and up would be the ticket. The most popular are the 300RUM, 7RUM, 300WSM/SAUM, 7WSM/SAUM, 7STW, 300 Win Mag, 338 Win Mag, 338RUM. So take your pick.
I would also look at the savage,and take alook at the weatherby sub moa vanguards. As for caliber I would look at 270, and 25-06 both will give you great performance for what you want. Scope, Nikon is best bang for the buck, as for the spot on I like the nikoplex and use turrets. I also have the bdc that also works well.
Ooooh, my bad, forgot about the 270 and 270WSM. Both excellent caliber. If you want a rifle on the cheap and option to upgrade as you can afford w/o the use of a gunsmith, the Stevens rifle is a great option.
Welcome to LRH, lot's of information here. Read all you can, soak it up. When you decide on your rifle/caliber and scope, then practice, practice, practice. Consider reloading also. It will help you in the long run, in more than one way.
For factory rifles, do you prefer sporter weight barrels or varmint profile? I haven't hunted with or owned a sporter weight barrel in 25 yrs. I, obviously prefer heavy barrels (HB). In that category I can and will recommend the Savage, Remington and Winchester rifles.
Scopes; I own a couple and would go with Leupold everytime. I own a couple of Nikon's and they work fine. In the daylight. Both are fine crosshair, one has a target dot the other does not. Early morning, late evening, they're useless for putting "boolets" on game IMO. I tell people, the bottom line with scopes; if you can't see it, you can't hit it and you sure as heck don't need to shoot at it.
Caliber; this category is as varied as the other two, as most any will do. By that I mean, if you shoot an animal, any animal, through both lungs, it will die. Shoot it in the heart and it will die. The brain, spinal column, same thing. They're going down. Not being a smart ***, just looking at it from a realistic standpoint. None are immune to high velocity bullets.
Most of the bottleneck cartridges, from 24 to 30 caliber, will get you from 0 to 500 yards with little difficulty. Having owned, reloaded for and shot several calibers at the same time, I have found that the trajectory of these is very similar. Especially if the rifle(s) zero is the same, velocities similar and you're dialing MOA.
Consider for instance, the .243 90gn NBT @ 3180fps and 6.5-284 120gn NBT @ 3145 and .300WinMag 185 Berger @ 3095fps, all with 300yd zero's. At 500yds the .243/90 drops 27.9", that's 5.3 MOA up. The 6.5-284/120 drops 26.0" or 5.0" and the .300/185, 24.0" or 4.6 MOA.
Not a lot of trajectory difference there. That's just under 4 inches of difference at 500yds between the .243 and .300. A lot of people can't even shoot a four inch group at that distance. What will vary is the amount of energy on target and on your shoulder. Just some food for thought. JohnnyK.
Get a savage with the accustock and accutrigger. Get the 270 wsm and shoot the 140 grain Bergers. Deadly combination. That's my current long range rig. Shot my deer last year at 825 yards. Smoked him. I put a vortex viper on top. Great scope for the money. Just my 2 cents.