You already had good answers but I would like to add my two cents:
The "starter set" is the cheaper option (less than 20$). It has a small prewritten adventure, a set a prewritten characters of level 1 with backstory, and the basic rules you need for this adventure.
Good point for it: cheap, the bare minimum you need to dive directly in it, already contain an adventure so it's easier for you as a new GM.
Bad point: it only contain a small subset of the rules, and will become "useless" if you decide to go further and buy the full books. Also, if your wife or kid do not like the pregen characters, you will not have the full rules related to character creation.
Then you have the core rule set already linked.
Good point: everything you need for a very long time, you will have all the rules to run anything you want. Other books are "only" going to add more options (spell, items, characters building options, ect).
Bad point: the price (120$), more information so it may be harder to digest everything and "get into it". It does not contain pre written adventure. You will have to find one separate or make one yourself, there are some free options available.
On top of that you don't need anything else exept pen and paper. Dice are of course greatly recommended, but you can start with some free phone app.