As heavy as you can comfortably carry.
I have a general rule of thumb with hunting rifles, when it comes to muzzle diameter.
2X the diameter of the bullet diameter.
The only exception would be .224 diameter barrels, where the minimum would be .500 inches.
As for contour, I seldom turn my barrels to the offered commercial contours.
I find that a barrel tenon/shank length of at least 1.5X the length of cartridge to be optimal for barrel stiffness and consistent accuracy.
Then either a straight taper or a contoured taper to the muzzle.
If you aren't planning on turning the contour yourself, pick a contour that closely matches the above and all should go well.
The nicest thing about such contours is the rifle balances between your hands in most practical hunting situations, especially for an offhand shot.