(Deer & up), I am assuming you are in reference to NA game. Your choice will do just fine.
Actually, alot of rounds will work, including some rounds mentioned like the Whelen for many people, depending a great deal on where you hunt. A med. bore like the Whelen, a big bore like the 45-70 & others are great to have in a rifle battery & could be that one rifle
for some situations, but not even close to all of the situations that I encounter beyond 300 yards & yes I have shot several beyond that & yes I was hunting & yes I am a bow hunter too. Some of the rounds like the 338WM, 8mm Mag, 300RUM & others can have a good niche, but again not the "one rifle" I would want. The 300WM would fill that bill for ME better than most, but one like mine (26"Sendero) is a little bigger than many would like. A 24" Medium taper would be a good compromize & that is what you wind up doing with one rifle. A "trajectory magnum" like the 7RM, 270Wea., & others are nice, but a little lite for Big Bears, Bison & such, although they will work with the right bullet.
So for this "one rifle" deal, I don't want it to be "substantially" bigger than needed 80% of the time, yet big enough for all NA game. I want it to be flat shooting, though with good optics & a good range finder I would not have to have the flatest shooter to shoot at long but sane yardages. To have only 1 rifle I need to be able to shoot alot & not erode the throat fast & that does away with a big mag.
Yes, Wyohandi, your round actualy will fill that bill nicely. I have a rifle that for me at least is even better, even though I own way too many rifles & will not use just one. One of my considerations is to be able to hand my guns down to my 3 boys & I am leaning more toward my main rifles being able to shoot factory rounds & esp. rounds that will always be available. For my use that rifle hands down would be my Win Mod. 70 30-06AI. It started off as a featherwt. & then a Brown Pre. stock was added. Due to the fact that I can seat a 180 out pretty far, coupled with the AI case I will roughly equal the 300SAUM velocities, in fact the SAUM & 30-06AI case cap. is a dead heat. Yet I can shoot fact ammo, yet with my loads with a 180 at 2,950 it is a flat shooter indeed.