If I was looking for a new rifle today, I would first think about what I was going to hunt with it (large, medium or small animals). I would then choose a caliber that would fit my choice. Yes, you can probably find one that will do the job on all north American game.
Once you have the caliber, it will simplify the search for you rifle ( long vs short action). Now the hard part, picking the right one. Off the shelf, made to order or completely custom....depends on your budget. There are quite a few made to order choices out there like Christensen and most will work with you to get what you want. Won't come cheap tho. Total custom is tough because the really great smiths are expensive and take forever to get you your gun.
If I was going to choose one for my self, it would be difficult. Because I believe stock fit has a much to do with accuracy as ammunition or optics, I might very well decide to make my own stock. Most people can't do that, so they will have to make sure you get correct length of pull, drop and butt angle.
Do tour research, get references and save your money!