Is it possible to play ME3 and enjoy it without playing the first two? Or will you be completely lost and have no idea what's going on
Depends; if you just want to shoot things and not pay attention to the story and treat it like a typical FPS, then it wont matter, if you are looking to pay attention to the story (it is a very good story) and treat it like an RPG then I would start with the first one.
It is a great trilogy and for as much flak the ending got it is well worth a playthrough from beginning to end.
I dunno... Nostalgic feel and way more things to do I guess. I've already done 3 1/2 playthroughs and still play it every once in awhile. Meanwhile, i couldn't even get halfway through a 2nd playthrough of ME2. Also wasn't incredibly linear like ME2.
I still consider ME1 the best of the series, and one of my favorite games ever. It was a little rough in some areas (although I think the complaints against the combat are overstated), but it easily had the best story of the 3, the best villains, the most customization in weapons/powers, and the only game with a sense of exploration.
ME2 is a solid game in it's own right, but the main story was pointless and it got rid of too many gameplay elements for my liking and it removed exploration altogether. Without the awesomeness of the Suicide Mission I wouldn't consider it as that much better than ME3.