This is a bit pathetic, but the first I would have heard would have been Beverly Hills. The first I got into was My Name is Jonas when I heard it on Guitar Hero III. Then one day I saw Blue for sale at Hastings, and nothing has been the same since.
It's been so long ago that it's hard to remember.
I was really heavy into Soundgarden and Pearl Jam, but was mainly a VanHalen fan back in the early 90's. I was still recovering from hair metal and was really angry for no good reason so I liked grunge a lot.
I remember hearing Buddy Holly and singing along to undone as I crisscrossed the country in my first car on backpacking adventures as well as in traffic to and from work.
I had a crappy Kraco stereo with a pair of 6x9's in my 70' Mercury that buzzed with the distortion when I cranked it up. Whether it was Undone or BH, I was sold. They were the soundtrack to some of the most glorious adventures of my newly found adulthood.
The first Weezer song I heard was Only In Dreams in a Modern Warfare 2 montage. I loved it so much that I went out and downloaded every Weezer song in existence. Best decision ever! Only In Dreams is still my fav :)