Rent.

You can't fold the origami it comes with if you rent. Just saying. 
 
Or you could wait the Bombcrew's PDF bootleg.

Rent it, it's a great game but you're probably not going to want to play through it multiple times.

Buy it, there are heaps of endings and its just so good you have to OWN this game.

Rent.

Reasons to rent: 
 Short, can complete in a few days, will likely be compelled to do it in one or two sittings. 
 Replay value isn't necessarily the highest for everyone, as the big reveals kinda ruins more than maybe 2 playthroughs. 
 
Reasons to buy: 
Origami :P 
An amazing game, and you may want to support developers that do this kind of thing, if you have the spare cash. 
There is some replay value for some folks, it's worth at least 2 in my opinion.  Plus some poking around scenes. 
There is DLC coming out over time, you'll miss a lot of this if you just rent it and send it back. 
 
Make your own call, but the DLC is one of the bigger reasons for me to buy this.  If you can rent it from Gamefly and keep the used copy, that's probably the best of both worlds (significant discount and you get to keep it still).

The only reason you would rent this game is if you're an empty soulless husk of a human being who doesn't know true emotion. Come on, this game is amazing and NEEDS to be supported, if the core gamers aren't going to do it then who? Don't rent it, that's seriously weak.

" Is it short enough to complete in about a week? "

Rent.

BUY

If you have the disposable income you should buy the game.  Support the developers, that's the biggest thing.  You also get a class game that'll still be generating discussion years out when people look back at Quantic's older works or highlights from the Playstation 3.

Having bought it and just beat it...
 
even tho you seem ready to buy it...I'd say rent.  If you are a like me and can beat it within a week, do so.  One playthrough and you won't want to play it again.  I don't want to have to fake my choices in order to see an alternate ending, personally.  I made every decision based on how I would handle the situation coupled with how I felt the character would react.  It just wouldn't feel right to purposely go back and do things differently.

buy it, i am liking the game so far. i have heard that it is short but still. there are like 20 different endings to the game.

  I'd say buy it. I really think it's the kind of game you'll want to revisit every couple of years, even just to play the same and keep your original playthrough canon. If in say two years you wanted to buy it for a replay it'd be a real bummer to find a similar situation to old Team Ico games for example, which tend to be very hard to find, and even pre-owned end up costing well above the original RRP.