Well, the first question is at what distances you plan to use it at. A 1.25-4x20 optic might be great for close-range shooting, perhaps out to 200m for general purpose work. On the other hand, a x50 magnification scope may be pretty useless for any sort of moving targets, or most other shooting at less than 700m or so, you might see a coyote and shoulder the rifle and all you can see is vague blobs of fur or you get lost in the trees and can't navigate the scope onto the right spot. 3-9x30 is one of the most popular, it's a modest range of magnification, with a medium field of vision. 4-12 is also very popular for coyote shooting, on x4 it's got a decent field of vision for scanning around, and then you can zoom in to x12 for precision work.
There's also a variety of fixed magnification scopes, for an absolute minimum amount of things to fiddle with.
Next is if you want exposed or covered turrets. Those are the knobs used to zero your reticle. Exposed knobs are great for if you're doing distance precision work in variable conditions. If you've got a head for numbers they allow you to calculate what is needed to put your point of impact on your point of aim. Some people don't like the style of exposed turrets, and there have been incidents of the knob rubbing on clothing and ending up on a different number than where it started. Most covered turrets can be adjusted fairly easily with a quarter or somesuch, but are a bit cumbersome to be fiddling with when you have to keep unscrewing the cap.
Next is reticle choice. That's the crosshairs. There's probably hundreds of different styles, some are basic + crosses in the middle, some are dots, some are more like ^. Aside from reticle shape, there's also a great many choices of thickness. Thin reticles are great for precision target shooting at far distances, but sometimes can get lost on backgrounds other than the plain white of a target paper. At the same time, thick and bold reticles are great for being able to spot on uneven and chaotic backgrounds such as in the woods, but might completely cover small or distant targets. On my AR15 I have a red dot scope and the reticle is a 4MOA glowing red dot. Fantastic for close range dynamic shooting, and very easy to spot on almost any background, but at the 300m range it completely covered the gong. I could not see the target at all, let alone try to do any sort of precision shooting.
Some scope models come with the option of mildots, millradians, ballistic dots, drop compensations, and other ranging marks. These allow for some quick and rough calculations for shooting under different conditions than how your scope is zeroed. Some people don't like them, it's largely personal preference. If you don't like them they're seldom so obtrusive as to make the scope unusable.
A related issue is First Focal Plane versus Second Focal Plane. FFP reticles will grow or shrink depending on the scope's current zoom. Most of them are designed with the highest zoom in mind, I took a look through some high quality FFP scopes on low magnification and could not even find the reticle on the gunshop wall. However, if you know what you are doing FFP reticles with things like mildots or other ranging marks can be used to determine the distances to objects being viewed. That allows for things like accurate holdover, where you intentionally aim somewhere other than the intended target, and use the measuring marks to hit the intended spot without having to adjust your scope's turrets.
Second Focal Plane reticles will appear to remain the same size on all magnification settings. Some people complain that they're not ideal for precision target shooting due to the fact that the reticle may eclipse the target.
Mounting options are also important. Some guns need very high mounts in order to get proper positioning, and optics with large objective lenses such as a 16-24x50 or something generally also require high mounting. There are several types of receiver rails you can get, with varying degrees of tilt on them to make it easier to shoot at further distances. 20MOA is a common one, it basically takes the angle of your receiver while aiming 20MOA above the target, and makes that parallel to the ground for your scope. They can cause complications when trying to aim at very close targets.
There's one-pieces bases, separate rings and mounts, and all-in-one combination bases, mounts, and rings. Some have features such as windage adjustments, slots so you can peek through like iron sights, or the ability to be removed quickly or even flip off to the side. My recent standards have been Leupold PRW rings. The bottom ring has a clamp for mounting onto a picatinny rail, which most of my recent guns have come with. The benefit of this is that I can move them around on the rail to find a good spot before tightening them on, unlike rings that mount onto the holes drilled in the receiver and cannot be moved around without drilling new holes. Which ones are best for you is a very personal question, and depends on things like if you plan to hand-feed bullets into the chamber.
And then budget! Optics range from just about $10 to just about $100,000, with as many bells and whistles as your heart could desire. Generally speaking, it's best to buy from the top of category A rather than the bottom of category B, if that makes any sense. Buy a high-end inexpensive scope rather than a low-end expensive scope, but it's usually best to buy at the top of your budget. Poor glass quality and imprecise tolerances are horrible things that I don't wish upon anyone. What works for one person's eyes might not be good for yours. I've seen a guy try out a $600 scope and a $2500 scope and he picked the cheaper one because his eye liked it better, sometimes you get lucky like that.
Warranty and whether or not it'll do you any good is also worth consideration. Some manufacturers have 100% no questions asked full replacements forever, others only cover a few limited types of potential issues for a short period of time. A great warranty isn't always useful, if you need to send the scope to the other side of the planet for six years to get it replaced.
The most recent scope I've bought is a Leupold VXR 1.25-4x20 Firedot, it has a button that activates a glowing red dot in the center of the otherwise normal reticle. Not the best coyote scope by any means, but a quite excellent close range option to my eyes for $720. It was the first time I spent more on the optic than on the rifle.
