I've got GRAW, DOA4, Madden 07, Hitman, and Lego Star Wars II. I love all of them - Lego Star Wars is a blast, and if you're a Star Wars fan there is a good chance that you will like it.
I was a little disappointed in Madden, but it's still pretty good. I think they tried to do a little too much on the play-calling screens. Once you are playing it's pretty sweet, and the mini-camp games are a blast.
DOA4 is a fun fighter, easy to pick up and play but hard to really master. My fiancee beats me 7 out of 10 times.
GRAW I haven't played as much as I should have, because it's awesome. I think it's the best FPS on 360, but I haven't played Prey (is that a FPS?).
And Hitman is fun. I never really played the others in the series, so I can't compare and it isn't "stale" as some might say. I love all the different ways you can accomplish the missions.
I'm playing Lego Star Wars II the most right now - it is too much fun.
I had Tomb Raider and finished it, but didn't keep it. I also had Fight Night and Sant's Row. Saint's Row is a great game if you don't mind the gratuitous language/drugs/sex glorification. I did so I traded it in...
As for going Live, I think it depends on what you like. The poker game can be fun as an easy multiplayer pick 'em up type of game, as can be Uno. It's nice to be able to download demos and arcade games. I've downloaded and tried just about every demo that was available.
For about $4 a month, if you already have a high speed connection, Live really isn't that expensive. Just don't go out to get one fast food meal once per month and it's paid for...
gamertag is whudats, by the way...