Yes, please do not go cheap now. You have a great rifle, I also have a 700P and love it. Its accurate, if I do my part it rewards me. I went with a Leupold one peice mount with low Burris extreme rings on a 40mm scope.
Below is copied from a optics website for the Remongton 700:
RIFLESCOPE RING HEIGHT
50mm riflescopes will almost always use HIGH rings in a given style. In certain instances, such as with extremely heavy barrels or some makes of firearm, SUPER HIGH rings may be necessary.
42-45mm riflescopes will almost always use MEDIUM rings in a given style. In certain instances, 45mm scopes may require HIGH rings.
40mm riflescopes will almost always have enough clearance with LOW rings in a given style, though MEDIUM rings will give slightly more clearance, particularly when using a barrel with a thicker shank portion or a heavier contour.
28-36mm riflescopes will almost always use LOW rings in a given style. Again, in certain instances of a heavy barrel or heavy shank portion of a custom barrel, MEDUIM rings may have to be used, but LOW rings will almost always suffice.
20mm riflescopes will almost always be able to use LOW rings, but in some cases may also use SUPER LOW rings. In this instance, bolt handle clearance of the OCULAR bell will come into play more so than objective / barrel clearance and should be carefully considered.
Hope this helps.