Years ago my brother was looking for a new rifle. He could only afford one this is the advise I gave him.
1) Get a caliber that will suit the largest game and longest distance you'll be shooting. (He choose 270)
2) Get a synthetic stock. I fairs well in bad weather and you can't scratch it.
3) Get a good scope with the right magnification (He chose Leupold VXII 3x9 he wishes he'd gotten 4x12). Don't buy cheep optics!
4) When you get the rifle and scope don't open the box! Don't fondle it, don't look at it. Take it to the gunsmith have him
disassemble it, clean it, adjust the trigger (most are too heavy out of the box), mount the scope, bore site it and make any stock adjustments needed for the barrel and action to fit perfectly. Then have him make sure the LOP is correct for you. If the stock has a Monte Carlo cheek if can be shaved to fit your face.
5) Break the barrel in correctly
6) Work up a good hand load.
7) Enjoy a gun that's been done right and fit to you.
IMHO if your not a bench shooter you don't need a custom rifle, you may want one and that's ok too! But do you need one?
Personally if you limit yourself the 308 I stay with the Browning also. In a bolt the 260 Rem or 6.5x55 might be a better choice.