I will agree with just about everyone here. all have made good suggestions. so I thought long and hard about writing this. I own several of the calibers stated. 223 WSSM, 25-06, 270 Win, and have owned but got rid of a 243 Win.
for my money, I would get two rifles. but since this is a one rifle for all that needs to be done.... I would have to pick the Winchester M-70 Super Coyote, heavy Barrel, 223 WSSM with a 1:12 twist barrel and the B&C composite stock. topped off with a Zeiss, Leupold VX-3, or Burris Black Diamond scope, 4-16 or 6-24 power range. I would go further and get a DE or Holland QD muzzle brake
on it. and get at least two bi-pods for it. one laying down.. 6-9, 7-13" range, and one sitting, 15 -27" for long shots. this will keep you from missing as much as you might if you free handed it. I would also get a sling to carry it or help your aim if you have to take a standing shot in the woods. I know my 1885 browning has never let me down with iron sights but that is just me, I am a die hard iron sight guy when it comes to deer sized or larger game. I leave the scopes for varmints and targets.
other good choices would be Savage arms, they have model 12's and 112's that will knock you socks off with accuracy. calibers would be 22-250, 243, 25-06, and 270.
Remington 700 SPS or BDL, VSSF, calibers 22-250, 243/6MM, 25-06, 270 win.
the varmint caliber I like is the 17 Rem, closely followed up by the 17 Mach4/17fireball. these calibers are tack driving machines if you even get close to a load they love.. My 17 Rem VS loves 25 grain V-max with Rem 7-1/2 primers and 26.5 grains of H-414. one ragged hole at 100 yards.. less than 1/4" holes at 200 yards.