Where's my hammer?!? ;-)Again, at the risk of being beaten with hammers or called an outcast - I do not like, nor advocate, buying a .22 caliber anything - ever. As I've said repeatedly, unless you're hunting rabbits or small game, it's a rather useless caliber to me and even more so in a SHTF scenario.
Having said that, for the price point you're at, the 770 with a basic scope on it is quite a bargain at that price - it's not going to be a great defense weapon like and AR or AK is, but it is a good all-around rifle that can reach long distances with reliability and put large game down to keep the family fed if you live in good hunting territory. As for the ammo, don't go nuts buying the expensive Wally-World ammo (and I would definitely go with .308 for what it's worth - just a better cartridge all the way around than the rather dated .30-06). Buy one or two boxes of the expensive soft-point stuff if you like, but you can get Russian import FMJ .308 at Academy for $12 a box, and better still, Sportsman's Guide has some fantastic zinc-coated Barnaul .308 (sold under the "Colt" name) for $10 a box and it shoots fantastic.
Good luck with the rifle, I don't think you can go wrong there, just get you a good semi-auto rifle or pistol as soon as finances allow to give you a bit more rapid-fire capability should you need it. ::redsnipe::
I've been putting food on my table for 40 years using a .22 rifle and a 12 guage shotgun. .22 for squirrel, rabbit, deer...damn near anything that will sit still for a minute. 12 guage for deer and birds. If you're open to buying used...you can get one of each and stay within your budget. Anyone that can't hunt and defend themselves with a .22...it's most likely more a matter of the shooter, and not the gun.