most places it is illegal to hunt with a rimfire firearm. you can hunt almost anything with a 12 gauge. from squirrels and doves or small game with #8. #4 for turkey or mid-ranged game. buckshot for deer and hog. and slugs for bear or very large game.
.243 is an excellent rifle for mid-ranged and up hunting.
.444, .4570, .50, 7mm is a good large game/ long range rifle. sniper
.22 or .17 is good for a trap gun. shoot trapped animals. also if they are not illegal in your area, they are good for small to mid-ranged game. shoot for the head. a .22 hollow point will cut a squirrel in half.
i like a .30-30 for a brush gun.
.410 shotgun is good for small game.
20, 16, 12, 10, and 8 gauge shot guns are all about what ammo you use. 10 and 8's are a bit of over kill, IMHO.
to my knowledge it is illegal to hunt wild poultry with a rifle everywhere.
now on the other side of the equation. when i was younger we used a .22 to night hunt deer. a round in the head will kill them. and they are so quiet that the shot is hard to place at night. not endorsing this but i admit i wasn't an angel when i was in high school.
for learning, start small. rodents first. then larger game. if you like fishing you will probably like fishing.
my opinion is if you are going to kill it, eat it. if you don't have room for 40 (yearling white tail) to 500 lbs (moose) of meat don't hunt deer. rule of thumb is it will dress out to about 60% of total weight of animal. if you are in it just for a trophy don't do it. good test is help clean a gut shot boar. if you still want to hunt go for it, and check your targets.
sorry if i sound preachy. just my views on it. hunting is great fun but i believe it comes with a responsibility.