I have recommended to almost all the beginners that I have mentored that they buy a bolt action .308. Very nice balance between power and recoil, and you can enjoy cheap and abundant ammunition compared to most other cartridges. I will always have a .308 in my lineup of primary hunting rifles. A 30-06 is just as good.
If you are fairly new to centerfire rifle shooting, please stay away from anything marketed as "magnum" - you won't be able to take advantage of any extra range offered by such a round compared to the standard cartridges already mentioned, and within normal hunting ranges of 250 yds or less ( not internet shooting distances, I mean the real world! ) the standard .308 ( or 7mm08 or .270 or 6.5x55 or .280 or 30-06 ) will be fully adequate for any moose and certainly for caribou. With a magnum you will have a more expensive cartridge with more muzzle blast and recoil, both hinder good shooting. Magnum rifles are, or should be heavier and longer, neither attribute is an advantage in the bush.
With a cheap, common caliber choice you can practise more, and use inexpensive surplus ammo for practise and switch to high quality premium hunting bullets for final sight in and hunting.
Tradeex ( a sponsor of this site) has a lot of very good used Husqvarna bolt action (mauser) rifles for about half what you would pay for a new, similar quality arm. They would be a good place to start looking. If you want to buy new, the Ruger already mentioned by a couple posters is a good choice, also consider Howa, Tikka, and the higher grade Savage rifles. New rifles with scopes offered as a "package" often have poor quality scopes, a mid-priced scope of around $300 ( or more) is more reliable and will last much longer than a cheap package scope. High power variable scopes are very fashionable at present, but you don't need more power than 6x for any moose or caribou hunting. Low power and the corresponding wide field of view in the bush is often a bigger advantage to a moose hunter than more magnification at long range. Standard 3-9x scopes are popular because they work well for most things.