I have a few rifles and I enjoy shooting all of them. I reload for all of them and just enjoy the challenge of working up loads that will group less than an inch. I have a couple of 7 mm mags that I load for and I enjoy them a lot. I also load and shoot for .243, 270 WSM, .308, and .325 WSM. I do a fair amount of deer and elk hunting as well. Bottom line is that any one of them will work for hunting. Well, maybe I wouldn't take a .243 elk hunting, but lots of folks around here do.
But the thing is when developing accurate loads, it takes a lot of experimenting and a lot of shooting. On top of that, it is more work to find a good combination of bullets and powders for the 7mm mags that I shoot. Whereas it's pretty easy to find a good shooting load for the .308 or .243.
My 7 mm mags are definitely versatile. But if I had to pick just one rifle that was easy to find good loads for plus be completely reliable in performance, I would have to go with my .308. As for long range performance, there are a lot of military snipers out there who use a .308 to make shots out beyond 1000 yards.
Just about any Savage rifle chambered in any common hunting caliber will do fine for deer hunting. Just pick one and start shooting. A lot.