At the moment I only own 2 rifles - a Rem 597 22lr and a FNAR semi-auto .308 - which I bought to learn to shoot with and protect hearth & home post-TEOTWAWKI respectively. I also figure on using the .308 to hunt for the pot. I also understand that the 22lr can be used to take small game animals and some varmints.

Question 1: While I figure a decently placed .308 round will kill a coyote, can I use the 22lr as well? If so, with what bullet at what range would I be able to do that (assuming the 597 liked to eat that particular round - Rem 597's can be picky about what ammo they like or so I'm told)?

Question 2: What do you suggest for the 597 to take squirrel, rabbit, jack rabbit etc.? Will a round nosed projectile do or do I need to see if the 597 will accept hollow points?

I have never hunted. Not any sort of bunny hugger just wasn't raised hunting and never had the inclination. If what I expect to eventuate DOES, then I figure I'll have to hunt to provide protein to feed my grandkids and as of wednesday of last week - 2/8/12 - GREAT grandkids. You folks are the ones who do it. I figure you are the ones to ask.

havn't shot many coyotes with a 22, too light
for distance.
but have killed a train load of rabbitts,squirrels and jacks.
shoot them in the head with what ever the rifle will shoot well

I'd use the .308 for coyotes. A .22 LR will kill a coyote, but it'll probably run a good long ways before it dies unless you shoot it in the head (and hit the brain). I'd keep shots on coyotes with a .22 well inside 50 yards.

For small game, I use hollowpoints in my .22s, even when I'm headshooting them. I've never had a .22 that wouldn't feed hollowpoints perfectly. I usually use CCI minimags for hunting. My savage Mk II FV shoots them into dime-sized groups at 50 yards.