As you don't have a shotgun certificate I doubt you will get far with anything but a .22 or 17HMR for a 'first timer'. You will need the land suitable as well. Anyway a .22 is ok for Fox but only close in, no more than 60 to 75 yards. But in truth you should not be setting out foxing with anything less than a .223, best of all a 22.250, but for now you are stuck with a rimfire.
I beg to differ - my Tikka 222 with 50 grain soft nose bullets is more than capable of despatching foxes out to 250 yards- 223 indeed
Les