So damn, two months before you can buy a rifle and even more time and paperwork for a pistol? Jesus, not even California, America's land of firearms restrictions, is that bad. You take a 10 minute multiple choice exam about handgun safety right at the counter and then wait I think 15 days before you can pick it up, and then you just need to show the guy at the counter you know how to safely load and unload your handgun.
And now, well, what's your intended game? Deer, elk? Personally, I'd go for something chambered in .30-06 as that round is very effective at most ranges and hits hard enough to take down elk while not overkilling against deer. It doesn't work so well at longer ranges as a .308 or one of the many rounds around 7mm/.280, but the increased velocity at shorter ranges will give you the extra oomph you need to help make that shot a kill shot.