Just looking for your opinions on the best all around rifle round. A well balanced round that won't kill your budget a the range but also will be effective to hunt a wide range of animals with.
I think for the purposes you specify....A well balanced round that is effective to hunt a wide variety of animals and is not expensive...assuming you are limiting the discussion to North American game. I personally believe that
the 30-06 is the best all purpose round.
However there are several others that will work almost as well or better; although each will have it's strengths and weaknesses.
Obviously the 308 will work, but you give up some performance with heavier loads.
The 7mm Remington magnum will work, you gain some maximum point blank range, a little energy, for the most part bullets with a little higher sectional density, but you loose bullet weight and diameter and it will cost you a little more.
The various 300 magnums all work well, but cost more, recoil more, and produce more muzzle blast. However they also deliver more energy and have a greater maximum point blank range. In truth they are not necessary for the vast majority of hunting situations.
There are a number of wildcats that will do a good job, but at an increase in cost.
If you consider the larger bears and the African Plains game then IMHO the 338 Winchester becomes very attractive as does the 375 H&H magnum.
If you wish to hunt the really large game then the 375 H&H is the starting point, however I believe you are entering the realm where a hunter would be better served with more than one gun.
Good luck.