Hey sorry about another save game thread but I wanted to ask you guys one thing. I played and finished  the first Mass Effect on the PC but I had uninstalled it, including save games (didn't think I would need them) so I could have some more space. 
My question is that would you need the save games to actually play the game (I highly doubt it) and if not, would you guys think that this would change the story a whole lot, since they don't know about the choices you had made in the first game.

Well, of course BioWare will let people play Mass Effect 2 without a save from the first game. It would definitely change the story, because the game would presumably be going by "default" choices.
 
That said, I suggest you install ME1 when you get some space and attempt to start a new game+ ("Select Existing Career" when starting a new game). If you are able to start a new game+ with an existing Shepard, the game has retained your "final save" files that are created when the credits roll. The reason I suggest this is because even if one were to delete all data in the Mass Effect folder on the 360, the "final saves" would still be there. 
 
Obviously PCs are more flexible and you have more control over what you can and can't delete, but it's possible that BioWare anticipated this issue for the PC version of ME1 and stashed the saves elsewhere.