Hard choice - - -
I intend to take my next deer with a .308. This is simply because I kinda, sorta, tentatively, decided to standardize on my Savage Scout as all-around rifle, and I have yet to shoot anything with it.
And, my long-time, all-purpose, do-anything rifle has been a .30-06.
But, since the question deals with medium game, my favorite has to be my .257 Roberts. It's put a LOT of meat in the freezer. I've killed several deer and three feral hogs with it. Both my sons took their first and some subsequent, deer with it, as did my daughter-in-law and a couple of friends. We call it our cheater's gun, because it is so easy to shoot well, and is very light-recoiling. It would be my choice for antelope and medium o large varmints, too.
Best, Johnny