@krico123 where will you be hunting mostly? I ask because both of those are great cartridges that you’ll be easily able to use for about any hunt in north america, but depending on where you are hunting and what type of hunting you may want a different scope. If you havent already, Id personally put as much effort and thought into a scope and mounts as the rifle.
Regarding the rifle, a tikka t3x is an easy good choice. A browning x bolt is a good choice. Both are within your budget, assuming that 800-1000 was a budget, and that your budget didnt include the scope and mounts—it was not clear to me if this was a budget or a statement that that was more than you wanted to spend. 700-1000 is about what a good quality new, off the shelf rifle will cost, with cheaper options being the “cheaper options” imo. Tikka and Browning are in my opinion the two best-value new, off the shelf guns that will last you probably forever. You can get cheaper guns, but most of those seem a bit more luck of the draw, a bit more rattly, etc—plenty of people use them, just haven't found one I personally liked. You can also get more $$ off the shelf guns, but those dont really buy better quality in most cases, usually just features or a specific configuration you may or may not even want, or a nicer-looking finish. To me those two are the sweet-spot for quality and value.
Wood is more expensive and isnt what sells in volume, so lots of gun stores dont stock many—but both tikkas and brownings and many other guns are available with wood stocks, so if you have your heart set on it you could find a gun you like and order one with a wood stock…just be aware it could take a while to get unless you actually make an online purchase and have it shipped to your ffl. Wood is classier looking, and it’s warmer-feeling if you’re hunting in very cold weather, and it has more soul than any plastic or fiber stock ever will, but apart from that there isnt really any functional advantage to it so it seems to have dropped out of favor.