It appears that MK has been such a popular fighter that it was ported to the SNES as well as the Megadrive at the time and a couple of follow-ups were made (even a movie I believe...).
If by "a couple follow ups" you mean eighteen of them (that's counting MK9 which is coming out in a few days).
I can't believe you never heard of Mortal Kombat! I was obsessed with it as a kid. I remember going to see the movie in theaters like ten times. And I had the comics and soundtracks and toys and stuff. Though I grew out of it soon after the console ports of MK4 came out. I don't think I've played any other MK game since then.
MK2 and it's ports are the best in my opinion (or it's the one I'm most emotionally attached to). But the ones to try are all the versions of MK, MK2, MK3, Ultimate MK3, and MK Trilogy. I think those are all the ones with that original digitized actor sprite style that you like. And they all have Liu Kang in it. He was the main protagonist of the story.
Sorry I can't give any real insight on what the best overall version is. It's been way too long since I played them.
As Bouvrie said, the SNES version of the first game is extremely censored. No blood at all and some fatalities are different. I think the Genesis port was censored too, but they included a "blood code" to unlock the original gore and fatalities.
Maybe see the first movie from 1995.
It's like the first live action video game based movie that isn't offensively bad. It's an overall decent and entertaining martial arts movie. But PLEASE stay away from the 1997 sequel "Mortal Kombat: Annihilation". One of the worst movies ever.
Btw, I don't think that gif of Liu Kang you posted is an actual fatality in the game. His real fatality in the first game is some pathetic cart wheel and uppercut.