My 2 cents worth is choose a cal that ammo is locally available , you will always find the old stand by, 308, 30-06 , 270 win , and usualy 7mm-08, 6.5 x 55 , and probably 6.5 creedmore. 303 British is always available and don't under estimate it's potential. Parker Hake made some very nice 303 sporters.
What takes your fancy? old school nice wood, deep blued steel , or plastic and a sand blasted finish ? My choice is wood and deep blued steel, it looks great and it does last a lifetime. My oldest is an 1862 Snider, wood and steel.
With Elk on the list just about any 7mm and up is more that enough, lesser can do it if you are patient for the right shot, not just any shot. you are never under gunned with a 7mm-08 .
A typical hunters rifle will never wear out , target, obsessive compulsive shooters do wear out barrels.
The used market here and on Gun nuts always has good deals on used guns like mentioned above. Tradex also has some good used ones too at good prices.
Starting out I would avoid Magnums, and hard to get caliber ammo, like the 7x57 , 9.3x62 and many more . Fun guns like a 30-30 /M94 are limited in range , they are not 200+ yard rifles.
What would I look for if I was you ??? Winchester M70, Rem 700, Parker Hale Safari/1200c , Savage 110? ,to name a few. {in a cal that is localy available above }
First choice would probably be a 7mm-08 but if the price is right a 308,30-06,270 ,all will be practical.
A duplex type reticle in the scope is simple and all you need for reasonable hunting distance. 3x9 is more than enough scope and will be available for around $200 new like the Nikon pro Staff. My favorite scope I have is a bushnel Scope Chief V in 4x40. I use lots of scopes from the 50's and 60's , that still shoot true. There are good scopes available under $300. Lots of used rifles have scopes , that are quite good. The old Bushnell's and weavers have stood the test of time.
Personal taste is on you as to action, style etc. you like.
New is a nice feeling, but a well cared for rifle, more classic rifle is hard to beat .
Good luck, take your time making your choices. Remember the rifle may put 3 in a single cluster in the right shooters hands, but if you are only capable of a 6" group no rifle will make it a 1/2" group, that's up to you.