Help me understand PS4

Hey PS4 community, Im looking to buy my 14 year old cousin a playstation either 4 or 5 (which is more worth buying) but I don't understand this whole monthly membership subscription. How does it work? Is it optional or does he need an account to access game, etc? Could some please try and explain it to me? What about games on CD are they still a thing? I don't know what games he plays but he's always wanted a ps and I want to buy it to him as a gift and I don't him to pay extra fees, his family struggles a bit financially.

Thank you

Edit: Everyone says ps5 is better so I'll start the search. Thank you all for the suggestions and the help. It made things clearer for me :)