night diving is certainly possible with a minimum of training
cave diving, on the other hand, is a long process, involving four classes over time (generally cavern, cave 1 (intro), cave 2 (apprentice), and cave 3 (full cave).
you're also talking about several thousand dollars in gear.
as far as recreational diving, the progression usualy is Open Water, Advanced Open Water, and Rescue
Advanced Open Water is somewhat of a misnomer, as it's not really advanced. it's more like Open Water Part Two. in it, you will do five specialities, such as deep diving,
night diving, peak performance bouyancy, etc. i would take this class before i
hit 30 dives or so. otherwise, you'll be wasting its benefits (if you wait too long, it
becomes redundant).
Rescue is an excellent class to take, and it works on your awareness and self-rescue
ability, plus CPR and first aid are covered as well (as a pre-requisite).
once you do those, you should get about 100 dives in to cement your skills before
thinking of technical diving (such as cave diving).
a great introduction of some tech skills and concepts is DIR-Fundamentals, offered by
GUE. i would recommend taking that class either for itself or as a great
stepping point to tech training (DIR-F is a recreational class, but it does
touch on some concepts and skills that will make future tech training much
easier).
hope this helps