Not saying it can't be done, but it's difficult to make a dual purpose rifle that checks all the boxes. Generally hunting rifles are light to medium weight. Varmint rifles are medium to heavy.

What you're trying to achieve can be done. It depends are what kind of hunting you're doing. If you're walking a half mile from the truck to the stand it doesn't matter if your rifle has a truck axle barrel and a concrete stock. But, if you're walking a bit then you'll appreciate a lightweight rifle quickly.

If there a budgetary reason for a one purpose rifle? If so, I'd suggest picking the rifle and stock that best fit the type of hunting you're going to do most often. If you varmint hunt year round every other weekend, then get a varmint style stock. But if you want to try to hunt a large selection of game very often then maybe a hunting stock is for you.

Not sure if you mentioned it in your post, but what size barrel does your rifle have?