I would look at something calibered in between .243 and .308 for your purposes. The .300 Win Mag would be overkill and expensive to shoot. I have a Savage Model 99 in .243 Win, an AR-15 in 6.8 SPC, and a Weatherby Mark V in .270 Win that I would all consider just about perfect for what you want to do, depending on what kind of hunting I was doing, environmental factors, and personal preferences. A big long bolt gun is a pain to carry around in thick woods and the scope I have on it would be overkill for the kind of short distances I would encounter, but it would be perfect for a treestand hunt overlooking a massive food plot or a coyote hunt in open country. Meanwhile, the AR and the 99 are both short, handy and fast handling- perfect for a deep woods stalk or a deer drive.
You would be wise to choose your platform first based on the kind of hunting you will be doing, and then begin to look at the issue of caliber availability in your chosen platform. There are many calibers that can do what you're looking for, so I would not get hung up on caliber as the primary consideration. Figure out what action you are most comfortable with for your purposes, then let that determine what caliber you want based on availability in your chosen platform.