Three basic sizes ... soprano, tenor and baritone. And there a little extras like concert soprano and things like that. Soprano uke uses C G E A tuning, which is a re-entrant tuning: the C is higher than the G. Tenor can use the soprano tuning, but it usually uses GCEA ... which can be re-entrant but often a low-G tuning is used. Baritone is just tuned just like the guitar's top four strings, DGBE; it doesn't sound very uke like at all to me.
Lyle Ritz is the uke jazz master. Also look out for Roy Smeck. And, of course of course, Jake -- who is just a monster player.
Google will find you vids, tunings, etc.
Here's a mixed bag of a bunch of different tunes ...
Alligator Boogaloo presents UKULELE BOOGALOO!