My first rifle, one that's still in the safe 40 years later, was a Rem. 700 in 25-06. Bought it as a kid with grass cutting money. While it was not the best choice for the type of hunting we do here in NE FL it did very good service on a bunch of hogs and deer over the years. Last dozen years or so it's been replaces by a even older .35 Rem that in reality suites the up-close type of hunting we do.
Started out using the 120 grain Rem. Core-Locks. Worked good. After a few years my dad bought a set of reloading dies for me and let me use his press. He also gave me a couple of boxes of Sierra 117 garin Game-Kings. He was partial to their bullets. While I can not say that it was due to the bullets as much as it was due to the care put into the reloads, by about the 3rd or 4th trip to the range it was obvious that those Game-Kings were VERY accurate. Better groups that the factory loads.
Of course with the close-in hunting we have here in NE FL I was never really at a disadvantage with the Rem. factory loads.
Stuck with the Game-Kings and never had a problem. Can't say that they worked "better" than the Rem. but they never failed.
After dad died I gave up on the reloading as I'm a hunter and he was a shooter, there's a difference you know, and I just did not go through enough ammo to justify the work. About that time I found the Sierra's loaded in Federal Premium factory ammunition. I've shot a number of boxes of it over the years. Not as accurate as dad's old handloads but more than adequit.
I'm sure than about any of the premium bullets out there will work, so long as you chose one made for deer sized animals. For my 2 cents worth I would stick with the 115 to 120 grain bullets..............