1. Story
2. Characters
3. Gameplay mechanics
4. Additional mode/features
5. Competitive potential

Because if the Story and Characters are not engaging then no matter how good the gameplay mechanics are you'll be bored out of your mind because you don't care for any of the characters.

You hit the nail on the head. Same goes for me as well. The gameplay mechanics can be incredibly ground breaking but if I'm not drawn in by the characters, the lore, the story then I'll never play it. It's what drew me to MK in the first place over the gore and the brutal reputation.

Characters
Story
Gameplay mechanics
Additional modes/features
Competitive potential

As you need characters for the story, they come first. You can't write a story and just throw the characters where you want.

Gameplay Mechanics. I don't care how engaging the story is, if the game plays like shit then the game is fucked. This is a fighting game after all.

Characters. Game should have a nice, diverse roster where each character offers something fresh.

Story. A good story would only make the game better and it certainly couldn't hurt the game. If the story itself sucks, the overall presentation should compensate for it.

Competitive potential is important, but not really for me.

Additional Modes/Features. Mini games and shit never keeps people coming back. Good gameplay will though so this is definitely lowest for me.

1 - Competitive Potential and Gameplay Mechanics on the first place as they are linked. Without proper gameplay mechanics you won't have a competitive game.

2 - Characters; I like the new characters and my old favorites are pretty much confirmed (Shinnok will make it, Shao Kahn probably not) but I am looking forward to especially the remaining new ones and their variations which will add more to the gameplay and gameplay is all I ultimately care about.

3 - Story; something I really like about MK and even more important this time around as they messed up MK9. It was pretty much a tie for me between characters and story.

4 - Additional Modes/Features; this is important and I hope for lots of fun stuff but again, all I ultimately care about is gameplay and a decent netcode. We can have a million modes but without a decent netcode they don't mean shit to me. Arcade and Story are confirmed anyway.

This is pretty much where I'm at these days. In my younger days, I was willing to grind through a bad game to get to the next plot point...not so much anymore. A great story mixed with great game play...that's how you get me(and anyone else for that matter).

1. Gameplay mechanics
2. Characters
3. Competitive potential
4. Additional Modes and Features
And last and Least. Story.

Were this early 2011 I'm certain story would have been number one.

1. Gameplay mechanics:
The most important thing about a videogame. It makes or breaks the game. Bad gameplay mechanics could possibly prevent future installments of the series, regardless of it's engaging story. Without working gameplay mechanics, you cannot progress in a story.

2. Competitive potential:
It irks me that this is listed as I see it being taken care of under the rule of gameplay mechanics. In terms of a Fighter, that's the whole point, to make sure the gameplay mechanics is in fine tuned so that it is competitive, so that it works.

3. Character:
Character is also important, the design of the character and what they do ingame (thanks to gameplay mechanics). Both of these falls into preference from the player. I have a friend who picks characters based on how they look, if they look ridiculous, he will main them no matter what and it actual works out for him. Competitive players select the most gameplay dominent (sp?) character. Then there's the casuals who play as the characters that fits their playstyle.

4. Additional modes/features:
This is where it determines the game's longevity. Because after the usual story mode is done. What is there left to do? Just your basic 1on1 versus mode.

Besides having bad gameplay mechanics, MKvsDCU messed up on replay value, which wouldn't matter for that game anyway. But it offered nothing much to do afterwards, just a tedious kombo trial that's borderline impossible and a broken online mode.

MK9 had a great chunk of content to last. A hefty long Challenge Tower mode. Want to test your character skils? Go do the last challenge.
Then there's Test Your Luck, where you fight against any character with random match stipulations out of your control, a good example of replay value and it's a shame that may not return.
Tag Mode to play COOPeratively with a friend, instead of against. Which I do with my not so good at the game friends in MK9, I even let them fight first, so when they get defeated, I'll win the round for us and tag them in. They have fun NOT fighting against me. This will be missed in MKX.

5. Story:
A terrible story line cannot cripple a game. That can be easily forgotten. And these days, you can throw in DLC story chapters to make up for it.
Bad gameplay mechanics however, will cripple a game, severly, there's no returning from that.
"Destiny", I feel, is a good example of this.
Terrible story.
Good gameplay mechanics.

1. Classic background fatalities
2. Story
3. Overall potential of characters
4. Online
5. Gameplay mechanics

1. Gameplay mechanics
2. Story
3. Characters
4. Competitive potential
5. Additional modes/features

(1) Story- The lore and Mystique of Mortal Kombat is very important. I know it's a fighting game, but it has always been a fighting game which has told a story. Think of how uninteresting the Armageddon story was. It made the entire game weak.

(2) Characters- I feel the same way about characters as I do about story. The old ones have to continue to develop and progress. The new ones have to be interesting and fit.

(3) Gameplay Mechanics- Of course, it is a fighting game. It needs to be balanced and accessible.

(4) Competitive Potential- I've never been much of a tournament player or anything like that. I feel like I may get more into that whole scene if MKX gives a good platform for that though.

(5) Additional Modes/Features- As far as gameplay, I mainly want the Mechanics to run properly and smoothly. Everything else is just icing on the cake. I wouldn't mind seeing a return of the free roaming, Deception style Konquest mode though. But that seems unlikely.

I really appreciate the feedback. To clarify, I listed gameplay mechanics and competitive potential as separate because I associate the competitive aspect with how balanced gameplay mechanics are. Sometimes, this goes against how interesting and complex the basic gameplay can be, the more creative and unique characters play-styles get they tend to be harder to balance and therefore lessen its chances in the competitive scene. Playing games casually vs competitively plays an important part in how we value these elements individually. Not all Fighting games are designed to be competitive and they can be really fun, but I completely agree that they tend to be deeply linked.

For me its

Story/Characters > Gameplay Mechanics > Modes > Competitive potential.

Gameplay
Modes/Features (Online)
Characters & Competitive potiential are tied
Story

Ive always loved MK's story and lore, but the game can exist without it. A fighting game lives and dies by how fun the gameplay is. Everything else is gravy.

I agree with this, only I'm reversing #1 and #2.