Are you newer to shooting? if so stay away from .300 win mag, too expensive to shoot and too much recoil., especially in a lighter weight hunting rifle. Think .308 if you are not yet used to shooting high powered rifle in the .30 cal class of cartridges.
Do you primarily want to hunt or target shoot.( when you say long range, how long, 1000yds?)
.300 Win Mag is a good round for what you want to use it for. Sufficient for any North American game.( would be my personal go-to round for most things if i didn't live in MA, maybe a little over kill for deer) I know a few people who have taken elk with it,it's certainly a good round for elk. It also will easily reach out to 1000yds and beyond. It has been popular with 1000yd shooters over the years. If you want to use the rifle for any truly long range shooting you will need at least 3/4 MOA accuracy, which is achievable in most modern rifles with match grade ammo.(probably have to hand load to afford shooting match grade stuff though) I load 180gr match kings with 71.6grs of IMR4831, seems to work good in my gun. Shot a .36" 3 shot group not to long ago. I'm getting 2850-2900fps with that load. I've only shot out to 600yds, it certainly does fine with that. I also shoot it a lot and am more than comfortable with the recoil.
Something like a Remington 700 Sendero SF-II would suit your needs very well, heavy enough to shoot from the bench,most are super accurate, and still light enough for hunting. Also, Mod. 700 XCR Long Range Tactical might work, depends on budget.
The Savage 110-FP would also be suitable, it has the heavy barrel, cheaper than either of the Remington 700's, and should be accurate.
.300 is also a bit of a barrel burner compared to, say, a .308.A heavy barrel that dissipates heat will generally be more accurate and probably last a little longer if you want the rifle for range use. Also, if you hand load, there is no need to shoot max, 3100fps, loads at the range, find a milder, accurate, load and your barrel will last longer.
the 111f is a regular hunting type rifle, light barrel, light synthetic stock, great for hunting, but will punish you at the range with the .300, and sufficient accuracy for real long range shooting may be hit or miss with that rifle. Something with a heavier barrel that's more target/tactical/long range oriented would be more suitable. Might be heavy to hunt with, but that's where you have to make the compromise. If you want to mostly hunt, then it's a whole different ball game, the light barrel hunting rifle would be fine.
Edit: 260 Rem is a good round too, would also fit your bill,probably will be my next rifle
