For just about any game animal that roams the North American continent it is difficult to beat the .30-06 cartridge. With bullets in the 125-150 grain range, at velocities at or near 3000 FPS, the .30-06 will handle just about any varmint, predator, or medium game animal (deer, antelope, etc) out to 300-plus yards. With bullets in the 165-180 grain range the '06 is fully capable of handling larger western mule deer, elk, or moose at any reasonable range. With bullets of 200-220 grains the largest North American game (including the great bears, bison, musk ox, etc) can be reliably taken.
Ammunition is available just about anywhere ammo is offered for sale. Reloading components are available in wide variety.
As for the rifle, just about any variant of the Remington 700 series, Ruger 77 series, Winchester Model 70 series, etc will provide very good performance at reasonable cost. Several years ago the NRA published articles rating factory production rifles, and found the Howa Model 1500 to be the most accurate production rifle (out of the box) on the market. The Howa 1500 was also marketed as the Weatherby Vanguard and S&W Model 1500 in years past. Moderately priced and highly regarded.