From your reply to other's advice, I am ssuming that you re trying to keep your initial purchase expenses a reasonable as practical. For sure it will be hard to be the oldie, but goodie 30.06 Springfield. Factory ammo is as readily available , and as reasonably priced for the 30.06 as about any these days.
A bolt action would be my choice beacause the it a is simple and reliable design, and usually a bolt action is going to be accurate.
As to the question of Manufacturer and Model. Depends somewhat on your budget. If you are wanting to stay at the "economy" end of the price range, do not expect any more than a Plain-Jane look, acceptable machining and a so-so trigger. But you should end up with good accuracy and a rifle that can last a life time with proper care and maintenance.
My expereince with the Rem. 770 is not good enough for me to recommend it. However when it comes to the Ruger American and Savage Axis ... I can. I have shot numerous of these two. The factory trigger is not all that swift on either, but it'll do. In fact I was so impressed with the Axis for the $$$ that I bought my grand kids each one. Both in 243 Win. Both grouped great with several factory loads I tried.
When it comes to a scope, just don't scrimp. Whatever your scope budget is, spend it all so that you get the best that you can afford. My expereince with low end scopes has been so poor that I recommend you avoid these like the plague. A good , economical scope .... Leupold, Vortex & Nikon offer decent scopes in the $200 range. I lean towards Leupold.
If you have the budget, a great buy in my book for a value scope is the Ziess Conquest. If I have read your hunting correctly anything in a 1.5-6 to 3-9 x 40 mm variable would be a good choice.