If there could be one famous musician I could see myself actually attempting to pursue, it would be Caleb from Kings of Leon. I love all of their music, from old to new, Caleb's voice has intrigued me, and I don't think I've disliked a single song off any album.
I think I'd be too scared to approach any other musician in fear that they'd think I was only doing that because they were in a band, but in this scenario, it would out of genuine interest to have a conversation with him (and possibly kiss his face). With most of the lyrics written by Caleb, I'd be pretty excited to just know what he's about.
Okay I'm starting to sound very very weird. Here's a video off their most recent album, and one of my favourite songs.