No shame in using a tripod! Also in a certain price range, let’s say 1200-1500 bucks you will have similar quality rifles so it is more a matter of preferences than anything else! 308 is plenty of rifle for deer and moose as long as you do your part and know your limitations(distance)! Buy the rifle that fit you the best, is the most confortable when you shoulder it! Then buy a good quality optic! Buy lots of ammo and shoot as much as you can, if you know someone that is a long time hunter shooter, ask questions, go to the range with them! Use rifles are sometimes a lot better than a new rifle for the same price!
This is as good an answer as provided so far. If you try the 308/30-06 and find the recoil uncomfortable, then look at the 6.5 Creedmoor, 6.5x55 Swedish Mauser, or 7mm-08. Still great performance on your mentioned game, with less recoil, and usually good ammo vailability...just might take a little more searching in more remote locations. And in long action non-magnum cases, the 270 Win or 280 Rem are also great choices. The 270 will have the edge in ammo availability. But as also mentioned above, fit of the firearm is very important; find one that fits you!
Firearm and optics quality will be dependent upon your budget. If looking for less pricey, the Ruger American does shoot well, and Howa's also shoot very well too... If you can afford better, look at Tikka, Remington, Winchester, Ruger, Bergara, or Browning. Moving up, you'll see Sako, Christensen, Antler Arms, Fierce, and others...where prices get pretty pricey. As with anything, if you can afford it, buy once, and buy right. It will save you money in the end. New vs used...depends on your priorities, but used can be a better bargain to get into a better grade of firearm (and optic). But get help from someone who is knowledgeable in current pricing of firearms and optics, or you may spend too much.
Old rule of thumb, spend as much on your scope as the rifle. If you can't see it, you can't hit it.
The advice of trying firearms before buying is good...and either offer to pay for the ammo, or buy your own to try in their firearms...or those that may be available to try at your local gun club.
Have fun in your quest!