RE: BROWNING BAR
I have a BAR .270 Win. (not safari grade) and have had great success with it.
I bought it ~10 years ago, New. Attached a moderately priced but "good enough" 3-9X40 Swift scope.
The gun has killed +/- 15 deer, from ranges from 5 yards to 400 yards.
It has never, not once, not during a hunt, not while test firing, never misfired or jammed.
Magnums like the 7mm Remington and .300 Winchester (and .338 Win for that matter too), simply because the spent casings are larger would likely be a culprit.
I have a cousin with a BAR .243 Win. and he loves it. Of course, he's a little guy (5-8 140) so avoiding recoil is more important to him than others.
You need to figure out what you're going to do with the gun, thus figuring out what the gun needs to do for you. Autoloading rifles where I hunt (NE Arkansas) where shots are just as likely to be 20 yards in the woods as they are to be 500 in a hayfield certainly have their advantages. But if you're going to hunt in big hardwood forests with little undergrowth, why not another action? If you're hunting huge fields out west (where the magnum calibers have much more value) why not just get you a used Weatherby Sporter in the .300 Weatherby or 7mm Weatherby Magnum calibers? Similar in price but the accuracy in the Weatherby will be superior and any potential resale value with the Weatherby will be great. The A-Bolt II is a similarly high out of the box accuracy gun with excellent resale and quite attractive. I've heard great things on Tikka's, but have never owned one.
Unless I was in Svalbard having to watch my "6" for hungry Polar Bears (in which case I'd carry a Mossberg 835, alternating 3-1/2" 00 Buckshot and 1.5 oz. slugs), and I wanted a magnum for versatile hunting or shooting, I'd go with the bolt action of some sort.