Figure you budget, you said $250, and look at scopes in that price range. Names mean something when it comes to optics. Buy a name you recognize. You may find some higher dollar scopes discounted. Now as for what to look for in a scope, yes the thinner cross-hairs will be best for your particular application. But of equal concern should be the scopes parallax and/or parallax adjustment you will want a scope with which you can set the parallax to the range you are shooting, at some point the parallax will be at X distance and beyond so you'll most be interested in having it where you can adjust to the shorter ranges.
Don't consider anything with less than a 25mm/1 inch main body tube, bigger is better. The bigger the objective lens(es) and ocular lens(es), front and back lenses respectively, the better the light transmission and the better the light transmission the brighter and clearer you see the target. Just about all scope's have multi-coated lenses so I won't go into that. You will require the windage and elevation adjustments to be in a minimum if 1/4 Minute-of-Angle, a minute of angle is approximately 1 inch per 100 yards of distance or 30mm per 100 meters of distance.
As for fixed versus variable magnification this is up to your personal preference. Fixed power scopes are generally thought to be more rugged but when dealing with the low recoil impulse of 22 LR in a target rifle I would not worry that point. A fixed power scope generally, there is that word again, generally gives you more optical bang for your bucks. Go to the store and if possible pick out two scopes from the same maker but with one being fixed power and the other being a variable, set the variable to the same magnification as the fixed power scope then looking through the scopes, alternatingly, and I would wager that you'll see the fixed scope to be brighter and possibly clearer/in focus than the variable. Note in some cases you will be able to fine tune the ocular lens by use of screw adjustable diopter, turning the rear lens assembly in or out of a finely threaded tube. If you choose to go with a variable you will need to be sure you get one that has the cross-hairs set on "The Front Focal Plane", by being placed there the cross-hairs will not get larger or smaller as the magnification is changed.
Now for a short bit on the rings. Use two-piece horizontally split screws on both sides of the rings, the bigger the rings and the more screws the better. A one piece mount is better that a two-piece mount. Tighten rings slowly and alternately, use an inch-torque wrench if you have access to one. Down here quite often if you have bought the scope and rings at the LGS they will mount them on the rifle for you for free which is a great deal.
Then comes the fun part, I mean that really, you now get to take the rifle out to the range and shoot it, sight it in initially and then find the brand and style of ammo she likes the best.
GOOD SHOOTING;
GLS
