If you can find all the features you want on an off the shelf rifle you are a lucky man, but if the $'s aren't a problem I suggest building a custom rifle.
Pick an action you like - push feed or control round feed, appropriate to the length of cartridge you want. I would try to find a square bridge Mauser along the lines of the Winchester M-70 or Brno CZ, rather than the round receivers of the M-700's or Sako's. Either way, proper bedding is essential to a stable zero, but the square bridge has more surface to contact the stock's bedding material.
A custom stock is a good choice if you are going to shoot with metallic sights as most modern off the shelf rifles are stocked with high combs for alignment with scope sights. If you like wood, buy the best you can afford, but good synthetics are cheaper and more stable than good wood, and cheap wood or cheap synthetics leave something to be desired. Take care to order the stock for a good fit. You might find that your hunting rifle requires a shorter length of pull than your target rifle - and take into account the clothing you will wear while hunting.
A trigger that is adjustable is important, but a non-adjustable trigger than can be tweaked by the gunsmith for weight, travel and over travel is acceptable.
Barrel length and weight are personal preference, but should not be to the extreme resulting in detrimental to handling. Barrel length may effect velocity, and barrel weight will effect handling. My own opinion is that far too much is made these days about light rifles, and I believe a moderately heavy well balanced rifle is superior to a poorly balanced light rifle.
I think a hunting rifle should have metallic sights as well as a scope. If in the future you wish to scope your rifle be careful not to over power the scope. A magnification of 2X at the bottom end is more useful than 10X or more at the top end, when mounted on a general purpose rifle. I think QD rings are a good idea, and I've had good luck with Talley. The scope on my .375 can be taken on and off repeatedly without a shift in POI. There are various makers of ghost ring rear sights if you like apertures. I discovered that a solid brass front sight gives very good contrast between the sight and the target regardless of light or the color of the background. It appears as black on white or as white on dark.
The choice of a sling and how it is mounted to the rifle should not be over looked. If you intend to shoot the rifle slung-up, the front swivel cannot be attached to the barrel, but if attached to the radius of the fore-end, when the rifle is carried slung on the shoulder muzzle up, does not raise the muzzle more that a couple of inches compared to the barrel mounted swivel. The Safari Ching Sling from Galco is an ingenious design which allows a single strap carry sling to be used effectively as a shooting sling.
I assume you have some ideas on the subject of caliber, but if not, the .30-06 offers so many advantages for the chambering of an all around big game rifle as to be the obvious choice. Save for the .375 H&H, any other choice will be "almost as good".
