Got a 40mm objective Nikon Monarch on the way, gonna upgrade to Loopy QD rings so I can remove scope when cleaning. Should I go with medium or low?

Is the rear open sight remaining? If so you may need high. Either way, there is a chance medium will suffice depending on your scopes eye relief.

I hope it works out for you. But I have tried and tried QR rings, and many other take off systems over the years. I like to shoot out to 225 yards, and I could not hold accuracy while taking scope on and off. IMO part of that is due to just taking scope on and off, and the other part is due to inherent stock weakness of MZ's. I do think a torque driver is a fantastic accessory for an Omega.

As far as the ring height is concerned. It is hit or miss. It depends on the length of the scope in relation to the front sight. And the eye relief you apply to the scope. The Low ringsshould work. Tom.

Selection

This would depend on where your stock comb puts your eye. When you shoulder the rifle with your eyes closed, then open your aiming eye, you should be looking right through the scope. Use the rings that do this for you.

Since, unlike the Germans in this regard, we consider a scope to be the primary sighting equipment, IF your rear sight interfers with mounting the scope at the correct place, you REMOVE the rear sight!! I have heard the various reasons why we need to have the irons as "backup" etc. In over 50 years of hunting throughout North America, I have only seen such a situation occur ONE TIME, when a guy dropped his rifle over the edge of a cliff! And he needed a backup RIFLE as well as a new sight!

Selection of scope ring height is far from "hit or miss". It is controlled by the height of your stock's comb and the bone structure of your face (where your eye ends up when you have your cheek where it is supposed to be on the stock comb).

I forgot to mention that this is going on my Omega. I guess the main purpose of my question was would I have enough clearance with low rings for the 40mm objective.

eldeguello has given you good advice about the stock and the comb. However I have found the comb's to be too low on most MZ's, and for most shooter's. The best thing you can do is to mount the scope properly(as close to the barrel as possible), and in proper alignment. Then do what you need to do to the comb to make it fit you. Normally a raised comb device is needed. This can be anything from moleskin to a leather cheek piece-depending on the height needed. If you make the gun fit you properly like I said, or if you make the scope fit you like eldeguello said, then you will shoot better.

Most MZ mfrs. make their comb too low, because it is easy to raise your ckeek slightly. But if they make them too high it is very difficult to lower your cheek. Tom.

That's the plan, as low as possible, if the rear site is in the way I'll take it off.

I always mount as low as possible/practical. I have used the Warne and Leupold removable rings in low on Black Diamond and Encores with scopes of 40mm objective. I also adjust comb hieght, they are usually too low. I shim with a wedge of foam under an elastic cartridge carrier. I always fit them to the shooter.

I have low rings on top of the one piece weaver rail. My scope is a 3x9x40 bushnell. I also had to raise the comb using a cheek pad from Cabelas by 1/2 inch to get proper alignment on my Omega. I do not have the thumbhole stock so I don't know how that would line up.

edit: I also removed the front and rear sight. Didn't think there was any need for them with the scope there.