My experience is in no way as big as some on this forum. I shot a few deer here and in England. I've always aimed in the line of the front leg on the middle of the beast. In case of an angle either on the point of the shoulder or trying to break the opposite shoulder. I've had very few runners with these shots.
My first love is the 300 Win Mag, but recoil is serious. If you want him comfortable you need him heavy or a stalker to carry the rifle , sorry guys. I plan to buy a 308 , just to play around with it. Just became member of a shooting club with long range facilities and for stalking. The 308 for diffrent reasons. I don't handload and think these ammo is available at reasonable prices. Recoil will not be to severe and so it will be a joy to shoot. I plan to build something lightweight. Probably 20" barreled Howa in one of Edi's stocks. This will be a rifle out of sentiment, just because I like it and to have some fun with. I already have a 7x64.
Purely for use on the hill, I still think that a good 130 grain ( Nosler Partition) out of a 270 is hard to beat. More forgiving if you misjudge the range.