for playable games on the PS4, there are quite a lot to mention.
for fighters, there are plenty of options to choose from. for the 2D ones, there are mortal combat X, injustice gods among us ultimate edition and injustice 2, blazblue chrono phantasma extend and blazblue central fiction, although the last one isn't translated to english at all, specifically the voice tracks. then there is guilty gear XRD sign, revelator, and revelator 2, however the story mode doesn't have any fighting at all, what you need to do is just watch the story until the end.
dragon ball fighterZ is also playable, the game will be released next week. for story mode however, I doubt that I think it will be pretty hard, like killer instinct's shadow lord story mode.
also there is street fighter V, marvel VS capcom infinite, and other 2D fighters.
as for the 3D ones, you can try dead or alive 5 last round, naruto ultimate ninja storm 4, one piece burning blood, tekken 7, and also the upcoming dissidia final fantasy NT.
for RPGS, odin sphere leifthrasir is the only playable action RPG you can try. it's a side-scrolling brawler with RPG elements like leveling your weapon, leveling your HP, acquirable skills, ETC.
for adventure games, there are a number of interactive movie point and click adventure games that you can try it out, however most of them need some patience and a lot of trial and error to complete it, except for some of them, like late shift or planet of the apes last frontier, which only requires you to watch and pick choices during conversations or events.
and if you are in to sport games, there is madden NFL 18, which includes accessibility mode like rumbles and some qewes. EA sports UFC 3 is also have some accessibility in it as well.
going in to the wilds, collecting pokedex, and capturing them are my kind of thing,
training them, making them evolve, and generally making them stronger is my ultimate goal,
fighting other manamon tamers, winning the tournament, and fighting octoros are what these manamons like to do,
and ultimately, I become the master of mana!