Hi Scott, I would advise you to forget about fox for a while,start out with rabbits but only after you have had considerable practice shooting targets.
A .22lr is a good beginners rifle but not really suitable for fox. The .17hmr is used by many on foxes but most would agree that you need to be experienced, have excellent shot placement skills and the self control not to attempt shots that are not ideal. The hmr is an excellent rabbit rifle, less prone to ricochets than the .22lr but is noisier and more expensive to run than a .22 if you are doing a lot of practicing.