Haha. I've done this before. But the songs you suggested in the first post might be too cheesy. I dont' know, it depends on each girl, so find out exactly what songs they like! I once learnt these songs to impress a particular girl: Marcy Playground - Sexy and Candy; The Killers - When You Were Young; The Format - She Doesn't Get it; Goo Goo Dolls - Slide; and Matchbox Twenty - Push. I'm sure lots of other girls like this sort of pop rock.
Btw this didn't really work for me, she just told me 'Wow, you're obsessed with me'.