Is this going to be a hunting rig?
If so, while Brad's choice is notable, I would also suggest looking into Talley. Their Lightweight aluminum rings are a solid solution. Another one I would look into is DNZ. Similar by design, although they have a cross member connecting the action and bridge together.
Without seeing the rifle and taking measurements, it is going to be hard to recommend a ring height sigh unseen. The Viper is available in several different sizes. Also, there are over 70 variants of the stock Remington 700 with seven different barrel contours.
Although, what you can do is measure the thickness of your bases. Then add the height of the rings. Note, you want to measure to the center line of the ring. Not where the scope rests.
Measuring the thickness of the bases plus the height of the rings and set that number to the side for a moment.
Then, measure the overall outside diameter of the objective. Not the lens, but the outside of the housing. If you plan to use covers, but them on and include that in your measurement. Then, take that number and divide it in half. Say it is 60mm, divided in half would be 30mm, right?
Now, take the sum of your rings and bases measurement, subtract it from the OD measurement.
If the number comes out positive, then you have adequate linear clearance. If negative, then it will be too low and scope will be resting on the barrel.
Oh, the other thing I just thought about, you may want to err on the side of going slightly higher due to the bolt interface. You wouldn't want to rotate the bolt to unchamber or chamber a round it doesn't hit the ocular housing.