I mount a lot of scopes and here are my suggestions.
1) I am another in the camp of using a pic rail with rings when at all possible. The big reason for this is, as mentioned above, the MUCH greater ability to adjust eye relief. When you look at fixed bases and the clearance you need to keep the rings away from the front/magnification adjustment the amount of fore and aft available is very small. As such, I will give you my two suggestions for a rifle like yours....
2) This is the solution I used on my new rifle. A good picatinny rail ( mine is a Tikka specific from Mountain Tactical) and the Vortex Precision rings that are made for them by Seekins Precision. This is a very solid solution with good adjustability. Rings and rail together should run about $200-250. Here are some examples
Vortex Precision Matched 30mm Ring Set• low .87 in.
www.scheels.com
This 1913-mil-std Nightforce standard duty base is made from aluminum, has 20 MOA, and fits Rem 700 long action.
www.scheels.com
3) If you want absolute bomb proof set up .....this is the set up from our inventory
Ring size 30mm<br>Cant 0 MIL/0 MOA<br>Height 30mm/1.181"<br>Length 126mm/4.96"
www.scheels.com
BASE REM 700LA 1PC-20MOA
www.scheels.com
Attached is a pic of my set up.....