When teaching a beginning drum student basic skills, I like for the student to use a medium weight stick such as any pair of 5B drumstick.
One determining factor for the weight of the stick will be the style of music to be performed. Usually, but not exclusively, rock music leans towards the heavier weights, while a lighter, more delicate stick, leans to the jazz end of the spectrum.
Rock is played loudly while jazz is played much quieter with a much more delicate, controlled touch.
Being a versatile player means having a wide arsenal of varied sizes of sticks in the stick bag. I may go from playing Friday night on a very loud sub gig in a country/ southern rock band, using a quite heavy drumstick (2B or it’s equivalent) and wearing earplugs, to playing a Sunday morning jazz brunch gig using pencils and playing as softly and quietly as humanly possible.
I usually leave the choice of drum stick tip (nylon or wood) up to the student with these pointers in mind- the plastic or nylon tip gets a better “ping” out of the cymbals but get sort of a flatter sound out of the drums while wood tips get more tone out of the drums and not quite as much “ping” out of the cymbals. Again this choice is a matter of personal taste and is totally up to what the player wants to hear come out of his or her drum kit.