Lots of choices here... Everything from .243 Win thru .260 Rem, 7mm-08 and 308 Win. My choice? 6.5 Creedmoor. It is a dead ringer for my favored 260, but MUCH more easily available in general and usually available in a very wide variety of loadings, everything from precision grade match rounds thru to premium hunting loads. Its more flexible and capable than the 243, but also easy to shoot and more than powerful enough to very reliably take coyote and deer.
Rifle?: Two choices. If budget is everything, it is VERY hard to go wrong with the Ruger American series. Buy in confidence and and call it good. Savage is good, but generally becoming over priced for what you are getting. inanition, the usual savage extractor design is flat out weak and crappy. I've bought several virtually new Savage 11 and 110 series that were traded in at a loss because the new owners found them unreliable with regards to extract and eject. $13 for parts and they run okay, but its still a really really shitty design that uses a sliding extractor, a small metal detent ball and a spring that looks like it came out of a click pen. No shit, it really is that lame...
If you/he wants a rifle with a bit more finesse, and is still and incredibly value for the dollar, the answer is Tikka T3X. Yes, its a common answer. Yes, they are that good. In my experience, the typical $699 T3X usually outshoots rifles far more expensive....
A Ruger American or Tikka T3X in 6.5 Creedmoor and a couple boxes of decent ammo are hard to beat. Do NOT NOT NOT buy a decent rifle, then cheap out an buy a lame scope. The tikka and a decent scope are going to run $1000. Forget a $700 tikka and a $150 Walmart low end scope. Better the cheaper Ruger with a decent Leupold VX3. He can do everything he needs to do with the VX3 2.5-8x or 3.5-10x..... Optics are usually an afterthought. In my experience, good optics are MORE important than the rifle. I've got $400 scopes sitting on top of $200 rifles. A low end scope WILL let you down....
I convinced a buddy to buy a Tikka T3X Stainless in 6.5 creed. We equipped it with a 4.5-14x Leupold Vx3 (too much scope to my opinion, but he purely hunts from box blinds over open fields). We chronographed about 10 shots with his preferred Hornady Whitetail 129 load (which I regard as 'bargain, low-end ammo") and send the info to Leupold for CDS caps. Once back, I installed the caps and he did some test shooting: One shot at 100 yards, one shot at 200 yards, one shot at 300 yards, and one shot at 400 yards, all off the bench, all dialed in using the CDS system. The end result was four shots, all inside the 1" orange circle target stickers he was shooting at. Can you really ask for more?