Dude, cavetown is a great musician and has some really good songs for ukulele. Also : If you find a genre you’re really interested in, search for some songs you like from that genre. Or start by artist (ie cavetown) and find a song of theirs you want to play. Or just look up the chords to any random song you really like. A few song suggestions:
“La Vie En Rose” by Edith Piaf
“Hey There Delilah” by The Plain White T’s
“Boys Will Be Bugs” by cavetown
“Me and Julio Down By The Schoolyard” by Paul Simon
These are just a couple I really like, I know they aren’t all contemporary. You could also look on YouTube for tutorials.