what game should i start playing?

You can get Heavy Rain out of your way faster than the others, especially if you do something wrong.

i'd go with either heavy rain or GoW3 first. i would personally play GoW3 first since it seems to have the least replay value out of those four games. 

Asteroids.

Just got Dragon Age and im loving it.
 

If you like Dungeons and Dragons type of stuff, Dragon Age.
If you like sci-fi Star Trek-like stuff, then Mass Effect 2.
If you like dramatic storytelling, Heavy Rain.
If you like action games and/or greek mythology, God Of War 3.

Do the shorter games first. 

flip a coin to decide between dragon age and mass effect

People should be banned for making topics like this. Seriously dude, no one is going to get into a massive discussion about what game this man on the internet should be playing next.  All your going to get is smart ass comments about games that aren't even on your list. I have complete confidence that you can decide for yourself which one of these games you should be playing right now. And if you can't, maybe you shouldn't be playing games that demand so much time.

Asteroids is a good choice

The Dragon Age.

" People should be banned for making topics like this. Seriously dude, no one is going to get into a massive discussion about what game this man on the internet should be playing next.  All your going to get is smart ass comments about games that aren't even on your list. I have complete confidence that you can decide for yourself which one of these games you should be playing right now. And if you can't, maybe you shouldn't be playing games that demand so much time. "

Mass Effect 2... or even Final Fantasy 13 is you have not tried yet.

Whichever one you want to play.

flip a coin dude.. process of elimination

ME2 and then Dragon: Age

GOW3

Hmmm just rent God of War its short !!, but killing Olympian gods has never been so much fun ;)

Mass Effect 1, then you'll know what is going on when you play 2