I have read this post with some interest, as I have been shooting nearly all of my life...(oldish git now) I feel I can add some pointers to what would be your best starter. .17 is a nice wee rifle, but I feel it is under powered (my own personal opinion) for starting out I would go with the .22 rimfire, this has all the stopping power you will need for rabbits, I have shoot foxes out to 80 yrds and killed they cleanly with this calibre, any further and I wouldn't attempt these distances.
If after you feel you want to progress to a bigger rifle I would suggest a .223 centrefire. this is an ideal varmint rifle for foxes, great when lamping at night.