Well, a very important thing to note is that some rings only work with certain mounts, so you need to make sure they're the same style.
Next is size, there's 30mm and 1 inch rings and you can do horrible things to a scope trying to tighten a 30mm ring onto a 1" tube.
Then there's height. Most types of rings come in Low, Medium, and High and that is an indication of how high above the mount the center of the ring is. What height of ring you need is determined by the objective lens of your scope, that's the last number in most scope specifications such as 3-9x30 which is most stereotypical hunting scopes. Trying to fit an 40 or 50mm lens in a low ring just isn't going to work unless your mount and/or rail results in the scope being higher than normal above the bore. I believe I have Leupold PRW medium 1" rings on my Leupold Mark AR Mod 1 3-9x30 and the objective lens is a bare millimetre away from the barrel. Low rings just plain would not fit, or I would bend my scope trying to force them on. I can't even fit a scope cap on there because there's no room. I don't mind it, but I'm sure it would drive some other people crazy.
Now if you want to get really picky, some folks(ATRS) say that rings with 1 screw per side are a better choice because it's easier to get them torqued evenly compared to multiple screws per side. Makes sense.
As a note for torquing scope screws, and screws in general, when you tighten one, it is essentially pulling down on that side which means the other side may tip up, or nearby screws might suddenly be loose. As such, you may need to leapfrog your way around the screws to touch them up and try to keep them even. My recommendation is to keep switching from one screw to its opposite, trying to keep them even. If you tighten one all the way down at first your ring will be quite a bit tilted in that direction. Go slow and check often.
I had to go over my Leupold ring screws four or five times before I was satisfied. Otherwise you tighten them all and by the time you're done the first one is now 10 in/lb loose so you have to tighten it a bit and then the second screw is now 7 in/lb loose and on and on.
As for brands, all of the major big name brands are generally decent. Leupold gets my vote because that's the brand I bought. Other ones should be fine as well. As long as you pick the right style and size and height.
Wait a minute, this is CGN, go use the search tool, noob!
