All the above posts have good choices. Your rifle make and model is more a personal choice, but I would like to throw my hat in the ring for caliber. I would suggest you consider the 6.5x55 Swedish mauser. It is a mighty fine caliber that covers all of your bases: low recoil, plenty of power for deer and even elk at modest ranges, one of the most inherently accurate calibers ever made.
I stumbled across a Kimber-sporterized version of the M96 in 6.5x55 with a stainless barrel and synthetic stock. After a little research I found out that they made these (still make some?) for a while, so there are some out there. The little "Kimber", as I call it, must weigh in at around a scant 6 lbs soaking wet with a 22" barrel and a 44mm objective scope. It shoots the 140 grain factory loads with very modest recoil, and it shoots sub-1" groups at 100 yards. Only problem is I can't pick it up without my 13 year-old daughter complaining -- it's really HER gun, and she loves it!
The .260 Rem is a very close sister of the Swede, so if you can't find a nice lightweight one like I did, you might go that direction.