- What are you going to shoot?
- Under what conditions will you be shooting it?
I probably wouldn't recommend a .17 cal. It does have the advantage of a bullet/velocity combo that works wonders when it connects with most varmints. However, it does have its drawbacks. First, you're only using a bullet that weighs between 20-25 grains. Despite their extreme velocity (3500-4300 fps!), it does not take much wind to buck the little sucker. Next, the extremely small bore diameter does not put up well with barrel fouling. The ballistics between rounds can vary widely which means accuracy suffers. Third, they are not suitable brush guns at all. Here, the bullet/high velocity combo works to a disadvantage. The bullets have been known to literally begin to fragment upon contact with leaves and grass!
The .22 mag is definitely a step up from the .22 LR, but again I wouldn't recommend it as a well rounded varmint cartridge.
Consider a .222 Rem or .222 Rem mag. (The only advantage to the mag is about 25-50 yards, the ability to handle a bit heavier bullet, and a few hundred fps.) They are fun to shoot and will easily bag coyote and smaller game. A 22-250 is another option that will add some range.
Are you looking for tips on make of rifle as well as caliber? My favorite Varmint getter is a Remington 722 in .222. Also, it's hard to go wrong with a Remington model 700.