My thoughts on your current list of choices...
1.I have some experience on the Marlin XL7s I really like them having setup and shot two both in 30-06.
2.I really dislike the Remington M770, this rifle was made for a price point and is crap. The Remington M700s and Model 7s are great stay away from M710s or M770s.
3.The Savage Axis is another made for a pricepoint rifle. Pass on this one. The Savage/Stephens 200 is also entry level, but a much better rifle from the same Company.
If I had only 300.xx to spend on a 308 Win I would be buying the Marlin XS7 in 308. Ruger now offers the Ruger American bolt action, but I am not sure if it is available yet in 308.
A rifle will last generations don't be in a hurry to buy it, choose carefully.