I have a few rifles, in fact the last 4 that I bought are living in my son's safe because mine is overloaded. Just yesterday my new custom barreled 6.5 PRC showed up and I'm not sure which rifle will go and "visit" my son to make room for this rifle. The 788 in my opinion is not something that I would build up. While functional, that is all it ever will be.
Now as to what breed to go with.... well that is truly a personal matter. Everyone has what feels best to them. I've shot some amazing groups with Brownings and Tikkas but I have sold everyone that I have had because they just don't feel good in my hands. My favorite rifle is an old Ruger 77 tang safety model and that is what my PRC is built on. Most people don't like the old mauser action but for me, when I throw one up and point it, I know that the odds are really good that something is going to tip over or I'm going to find a very small hole in the paper that I am punching.
My first criteria in a rifle, or hand gun for that matter, is fit. I say that because if you are not comfortable with what is in your hands, it's hard to overcome some of the other variables. (as to fit, I am very fortunate to have the tools and to have worked with wood and fiber materials most of my life so I don't actually have a single rifle that I hunt with that I haven't modified the stock for me.) The next value and almost as critical is the trigger.
Now when it comes to which caliber.............. here we go down the rabbit hole!
Over the years that I have spent guiding and hunting for elk, I have seen elk taken with everything from a 25:06 to the big Lazzeroni. Most any one will take an animal with the right bullet and the right bullet placement. Having rifles that are smaller in caliber and rifles that are bigger in caliber, when I personally head to the elk hills, 9 times out of 10, I grab a .300 Win Mag. To me it is the most versatile caliber with the ability to go from 110 grain to 220 grain bullets in factory offerings and more if you are a handloader. And actually the elk and deer that I shot with a rifle this year were all shot with a .300 Win Mag.
So don't know if there is anything in this long diatribe that is helpful but it's below zero here so didn't feel like working outside today and with a 25mph cross wind at my backyard range, not much good bench time either so I'm rambling on. Good luck and have fun with your picking of your next best hunting/shooting friend.