Savage, out of the box, from the major non boutique gun builders are the most accurate, consistently. If has to do with how they are assembled and head-spaced mostly.
The 110 is a great rifle.
I like the idea of the long action, as it gives you much better selection of calibers later should you choose to change from a 30-06 to maybe 300 win mag, and barrel changes are very easy, and can be done with great precision, at home, no machining required.
The Savage Axis is not the same level of quality, so I cannot recommend that line.
I am left handed as well.
When the shots are long, settle for nothing less than the precision of the 110 Tactical Desert Left Hand.
savagearms.com