Leupold VX ll is a great choice. I've owned many of this model.
The rings will depend on the size of the front or objective lens.
Take the scope and gun to the LGS, if you are buying a 3x9x40 a medium weaver type in matte black will probably work. I've owned several Leupolds in 4x12x40, they will do what you want.
If you are buying a Leupold in 4x12x50 it probably will take a high ring, perhaps an extra high.
Mount the bottom half of the rings. Put your scope in to make sure the Objective does not touch the bbl or the adjustment knob does not touch.
Also some gun/scope combinations may require offset rings so you can get the right eye relief. I've run into this and the barrel touching many times, usually after I am home and the shop is closed.
A good LGS will have a scope bar to ensure the rings are true so one doesn't get the ding in the scope body at the ring.
If you are going to order your rings this is a good place. I've ordered many things from them, such as Kahles binoculars, and like their service.
Weaver Four Hole Skeletal 1" Rings | SWFA
It also is a good place to look at all good rings, optics etc so you can see a good price and different models
The Weaver rings I pointed out are 30 bucks while Leupold Tactical's are 104 dollars. unless one is going full SWAT on coyotes or paper targets something the Weavers look very good.
One should be able to lift and mount the rifle while pushing slightly forward keeping your head erect, pull it back to your shoulder and have the center of the crosshairs in direct line with your eye which is looking directly at your target. The cross hairs will appear on the target like magic. No other movement like stock crawling should occur.
To summarize get rings that allow adjustment for your eye relief (front to back movement of scope in rings), right height so the scope can clear the rifle and give you correct eye positioning when you mount the rifle.
The last thing is have fun.