I mainly shoot a 7mm mag or an 870 slug gun for deer, but when I went shopping for a new, lighter rifle I made a spreadsheet that averaged out velocities, energy, and trajectory for common calibers from 22-250 thru 7mm rem mag. I looked at the numbers for factory loads of a specific types (ie. ballistic tips, bondeds, pointed soft points, etc. of all grains from all mfrs) and averaged across all factory ammo brands and picked the flattest-shooting, highest energy rounds. The top choices were:
1st 7mm Rem Mag
2nd .270 Winchester
3rd 30-06 Springfield
4th .308 Winchester
5th 25-06
Already having a 7mm Mag and a hunting equipped AK (Yes, I have taken deer with an AKM), the .270 also fit perfectly in the stable, filling a gap. Even if I didn't have the 7mm already the .270 might have been the choice. Of course, the 30-06 is the most flexible round there is, as far as weights and speeds available with factory ammo. So, the numbers say that you already own what is just about the perfect all around hunting caliber out to 300 yards: 30-06. It seems you'd want to go bigger, up to 300 Win Mag (flat shooting hard hitting round with monster recoil and price), or go smaller with a flat-shooting, accurate, enough-for-mule-deer 25-06, which is also pricey. For cost, a .308 can't be beat and it's just about as flexible as the 30-06, and even better if you handload (so I've read).
But these guys have way more hunting experience than I do. So take my engineering study with a grain of salt. The real world is quite different than a spreadsheet.