This coming from a guy who owns bolt and lever action rifles made by Remington (M700's) Ruger (M77) Savage (116's & 10"s) Browning (A-Bolt"s) Mauser (98 & 96) Marlins (X7 and 336c) and Tikka and reloads for them all.
My advice buy once cry once
Buy a stainless steel synthetic stock Tikka hands down the most accurate rifle I havecever owned or been fasrer and easier to find an accurate load for and is very very well made with excellent QC.
You will not be sorry if you buy a Tikka
If wood stock is your thing then Tikka makes both straight and laminate wood stocked rifles. In most people's opinions there is no better production factory rifle under $800 than a Tikka
As far as which caliber that's tougher than the rifle choice these days.
If your not recoil shy then I'd suggest 30/06 as every body makes great big game ammo in all the latest and greatest bullets in 30/06 and it will be on shelves in every last place that sells ammo
If recoil is an issue I'd suggest something like a one of the newer 6.5 calibers like the Creedmoor or the 7mm/08 is a great all around caliber just remember the lower powered non magnum calibers will have limits on how far you can take a shot on big boned big heavy game animals Ike Elk and moose
Others will disagree but I wouldn't if given a choice want to hunt and elk and moose with smaller calibers like a 243 yes if I for some strange set of circumstances had to choose to either elk hunt with a 243 or 25/06 or not hunt I would hunt with the 243 or 25/06 but if my choice were a 243, 30/06 or 300wm I grab the 300wm every time.
I know plenty of elk are killed and have been killed with 243s and 25/06 but the advantages a 180 to 205 grain bullet traveling at over 2500fps when it unexpectedly encounters an elk shoulder joint vs a 105-120 grain bullet speak for themselves.