I used to play Darkstalkers/Vampire Savior and The Last Blade way back then. Not really good at fighting games in general but I played most of the old ones. It's common to be at least "able to play them" when hanging out with friends. My current favorites would be Arcana Heart 3 and Dengeki Bunko Fighting Climax Ignition.
Let's start of by saying Mortal Kombat X PS4 is GREAT. The graphics are nice, the controls are intuitive and the sound is awesome. The storymode is nice and i'd even consider playing it more than once, even though I find it a bit short, a few extra scenes would have been nice. The X-ray and fatality / brutality moves are fun to watch and are detailed. The crypt makes you want to keep on playing, just to unlock every single grave in there. I would have given the game 10/10 if the storymode where a bit longer and if the "kombat pack" content would have been available from day 1. (personal opinion)
Without a second thought, Mortal Kombat Sega version was one of my favorites. I know I played more fighting games, but this one always comes to my mind first when I think of it. The moves, the fatalities, the brutalities, I think they were the first to create a fighting game with such things, and honestly, I've never found another game with those features since then. Street fighter makes attempt though.
Guilty Gear (namely the newest one, Guilty Gear Xrd REV 2) for 2D fighters. Crazy characters, awesome soundtrack, and fast and smooth movement.
On phone, I play Street Fighter IV Champion Edition free version on Apknite. But I honestly think it's one of the worst SFIV ports. That shitty background and the low res graphics screams laziness. If they made a port like the 3DS version, I would've bought it in a heartbeat.