..If it were me, and my father, I would look at a premium type of bullet in the 130gr weight, and never give it a second thought. I read an article a couple of years back, suggesting that might be the best weight all around in 308 for whitetails. I'd try to load them to about 3000 fps maximum...perhaps even 2900...
another approach would be a 150gr bullet, but load it down to about 2500-2600 fps. Recoil would be much less than a full-house load, but you would still have the heavier bullet weight, if that is an issue. Heck, people kill deer all the time with the "hand-rifles" in 30 caliber, and they are probably getting more in the 2300fps range.

"Progress, far from consisting in change, depends on retentiveness..those who cannot remember the past are condemned to repeat it." Santayana