A lot of focus and budget goes to the scope, the action, and at times, the chassis. Much like a car, the power (Calibre), the suspension (chassis), and your comfort and fit behind a nice dashboard (Scope equivalent) are key considerations... Did you look at the tyres and wheels? You can have an awesome sports car, but with cheap tyres and wheels that won't go far without an issue... guess what! Scope rings are equivalent to this analogy. Good rings are important to the overall application and the Calibre of the rifle. We will cover rifles, not the AR15 or AR10 platforms - bolt action primarily. So here goes a Tier One example of application and consideration to have a reliable and enjoyable time shooting.
Related Article - scope Features when Shooting at Phoenix Rifle Club
Planning your scope rings
Either you get to post on Facebook "what rings should I use for this rifle" and get 30 answers, to which you have to go through and see which one is the appropriate answer OR you do the math! It isn't complicated, but for some, it can be a brain puzzle. Don't be afraid to attempt the math - it is easy. Immediately, you can observe if you have a forend where the bell of the scope will be positioned, vs. a floating barrel exposed. That will give you the direction your scope rings will go. A forend takes up space above the barrel, which will require you to have taller rings for the clearance of the bell of the scope. The other is the type of rings you will want - a pair of rings, a cantilever monorail, or a Monolithic Short Saddle rail.
Measurements to gather
By now you have chosen your scope - another article will cover this in greater detail since there are a lot of parameters to consider. The dimensions of your scope to your rifle need to fit with the goal to be close to the barrel but NOT touching the barrel.
From the Scope: The main tube in Millemeters and the bell diameter are the two dimensions to gather.
From the rifle: Top of the Picatiny scope rail to the barrel where the bell will sit. Getting a rough idea of the eye relief will roughly indicate where the bell will position over the barrel.
Calculating the right scope ring heights: The minimum height is when the bell will touch the barrel, therefore you will have to have a ring height to be taller than that calculation. The Objective Diameter divided by 2 is the centre of the scope to the edge of the bell. Subtracting the distance of the top of the scope rail to the barrel gives you the minimum ring height. This applies only for parallel mounted scopes, that have no rail or scope ring built-in elevation.
(Objective diameter)/2 - (Scope rail to barrel height) = Min ring height.
Forends that cover the rifle will of course have a minimal and in some cases have no (Scope rail to barrel height) - so you are left with the bell radius driving the height of the rings.
Scope covers also have thickness - add that rubber hugging and cover height to the overall minimum height.
Ok - that was the manual way - you all want a link to add your dimensions in? yeah, I know - I could have started with that! Here you go: http://www.mil-rad.com/scope_ring_calculator
Adding additional elevation to the scope
For long distance shooting, adding an angular slant to the scope base rail, or the scope rings achieves additional scope internal adjustment for longer distance shooting. As an example the Ruger Precision Rifle in 6.5creedmoor comes from the factory with a 20MOA (Minute of Angle) rail. Tier One's Short Saddle can come in different built-in MOA to the rings. In the case shown below, there is 20.6MOA built in, and when together you have 40.6MOA in additional elevation.
Keep in mind that now the scope, when zeroed at 100 meters or yards, the scope's crosshairs will be centered and looking through the top-side of the front lens as the scope will look slightly angled down at the front of the scope. When this happens, YOU NEED MORE CLEARANCE! With the good old geometry class, you took ages ago, you have to figure out that additional minimum ring height on top of a parallel mounted scope. Doing this with the goal of having a bell close to the barrel/forend takes a bit more to calculate. Remember there is 60MOA per 1 degree of angle.
Additional min ring height = Length from the forward ring to the end of the scope bell x sin (MOA/60)
Example Element Optics Titan Scope = Total length is 385mm, the front ring will protrude forward by 185mm minimum from the front ring, with 40.6MOA built-in. So the math is 185mm x Sin (40.6/60) = 2.18mm
Is that head hurting yet?
Once you have done the math - rings are measured from the base of the scope rail to the middle of the scope centre. With your minimum ring height in hand you can shop for scope rings. Here are the considerations on the shopping and quality of the mount.
Calibre and mount type
The Calibre makes a difference on the impact force put onto the scope as the rifle pulls back, the scope being stationary will be yanked back. Torsional forces put onto the rings, as well shear forces at the rail between the rings and the scope rail will test both materials as well as the geometry of the rings used.
Small-Medium Calibres: A single screw mount at the rail, with 4 screws at the rings will mostly be adequate if the ring material is billet/stainless (hard metal). In my experience, I would go up to .308 with higher-end rings like Tier One where the tolerances and machining is high-end, and the geometry (wider length rings) grab onto the scope tube with a decent amount of surface area with the proper torque on the screws. Additionally, rings must have a Picatinny slot square key under the rings to fit tightly to ensure no slippage.
Magnum Calibres: Stepping up to 2 screws on the rail mount, and 6 at the rings provide a more secure and bigger area for the impact force to distribute. Again, that jolt force, especially with a heavier scope (if used on magnum Calibres to reduce the recoil some) is going to yank at the mount, rings, and the rail itself. Larger weight of scope vs. Bigger Calibre will equal larger forces on the rings and scope tube.
For the ultimate mounts, there are Long Saddle and Short Saddle mounts offered by Tier One, there are others like Spurh and the likes. I love Tier One because they have a one-step 5-axis process and their precision is just amazing. The tighter the precision, the better the geometry works to resist the impact force. Avoid cheap rings, and your zero will hold. Good beefy rings will handle minor knocks, and your shooting pleasure will be on the money every time. I have have seen/heard a few members having time-wasting and ammo-wasting experiences with cheap rings - don't be that person, save ammo and sanity!
The DO NOT DO's
Don't get rings where the base mount notch that fits in the Picatinny rail uses the "screw" which is rounded. The impact puts pressure at the top edge corner of the Picatinny rail against the screw which is round - this will mar the edge of the rail and damage it, all the while there will be more movement of your scope within the Picatinny rail slots. You want this to be a tight fit!
Avoid Split rings where the ring mount it at the top of the ring. You will have greater difficulty in mounting the scope, as well as you have a geometry where the scope being forced back is going to want to split the rings apart by the round tube. Side-to-side ring screw mounts distribute the forces equally on each side and evenly, placing less stress on the threads and the ring by using more surface areas to distribute the force impact.
Tightening screws require a torque screwdriver, don't skip this step! hand tight, or good enough is NOT good enough. If you want to maintain scope zero, even pressure, proper pressure to protect the scope internals must all be within specifications. Using the proper screw bits, and ensuring you have clean threads will give you a reliable mount, and long lasting accuracy.
Tape on the inside of the rings allows scope shift. Avoid tape on recoiling rifles, the scope eventually pulls at it, and the eye relief changes, and you get minor shifts in zero. Good rings have the right surface area, with good tolerances which achieve an even pressure on the scope materials.
Lapping scope rings - while it is a good practice to ensure proper scope ring alignment, better surface matching the scope, lapping rings can if not careful increase the diameter of the rings to where uneven pressure (topside and bottom) can be increased. Getting good precision rings will ensure the diameter is suitable and precise for your scope, and having a good scope rail ensures it is straight, flat, and with good tolerances.
Tier One Scope rings: https://tier-one.eu/
Good Scope Blogs: https://element-optics.com/blog/