I've never finished Assassin's Creed one, I've played some of it at my cousins, and I really liked it. I will most likely buy (or at least rent) Assassin's Creed 2. How important is the story to what will be happening in AC2?

I would guess very.  I mean, you'll still be able to have fun running around chopping dudes up, but you probably won't have a clue what's going on in the present day / Desmond Miles part.
 
I'd find a copy of AC1 and blitz through it, it doesn't take very long at all if you do the absolute minimum number of side missions and it's still a great game.  90% of the overarching story is learned from the Desmond Miles parts, so pay attention to that stuff.  Failing that, you can probably just go and read up on what happens in AC1.

If you want to understand the Desmond parts, you should play through AC1 and the Ezio parts most likely will have something to do with that also.

" I would guess very.  I mean, you'll still be able to have fun running around chopping dudes up, but you probably won't have a clue what's going on in the present day / Desmond Miles part.  I'd find a copy of AC1 and blitz through it, it doesn't take very long at all if you do the absolute minimum number of side missions and it's still a great game.  90% of the overarching story is learned from the Desmond Miles parts, so pay attention to that stuff.  Failing that, you can probably just go and read up on what happens in AC1. "

The new game will likely fill you in well on the essential story hooks you've missed. I wouldn't worry too much about playing the sequel without having completed the first game.

The first Assassins Creed is more an introduction so it wouldn't effect your gameplay, although i would consider you looking up any additional information on Desmond Miles as the sequel shall feed it's story lines off of the first game.

Given the shit that happens while in the "present" in AC1, probably super important if they go does the same story telling path in AC 2.