Did the launch line-up encourage me to buy the system, or was I going to buy the system anyway?
I wanted the system because it I really liked what it did, better graphics, built-in party chat and cheevos. The launch games weren't great.
What did I play the most at the time?
It was months before I got one (there was no pre-order, and everywhere was sold out), but then the game I played the most was Geometry Wars.
If I bought the console well after the launch period, what launch games did I buy, if any?
I had a deal from Panasonic where I could get essentially free rentals at Blockbuster video, so I rented a bunch of games including COD2, PGR3 an NFS: Most Wanted. I bought Geometry Wars.
What games do I consider to be classics?
I really liked Need for Speed: Most Wanted, I ended up getting 100% achievements on that one. Oh yeah, and Geometry Wars.
What games could I play years later and have fun, classic or not?
Geometry Wars.
Basically, the Xbox 360 launch wasn't great, but the system got better, fast. Guitar Hero 2 and then Gears of War made the system into a classic for me.
PGR3 was a big disappointment for me after how much I enjoyed PGR2. It felt like something was really missing.