Now that you have an uke, welcome to the party. The one thing I was really excited about when I first bought an ukulele was how "simple" it was. That statement underestimates this instrument, but in all fairness, it doesn't take much to get started fooling around with one of these things.
Prior to learning any chords, I loved the sound of strumming the muted strings. Like a half-effort chuck. The sound of the muted strings resonating in the tiny body of the uke sounds so great to me. Every time I pick it up, I can't help but strum the muted strings just to get a feel once again.
The first chords I learned are the chords I play nearly every time I pick the thing up. C major, G major, A minor and F major. By learning those four chords, you can play almost all songs known in the current music industry. Here's a list of 10 VERY popular songs with the progression of those four chords:
1) Hey soul sister - Train
2) Dammit - Blink 182
3) Can you feel the love tonight - Elton John
4) I'm yours - Jason Mraz
5) Somewhere over the rainbow - IZ Kamakawiwo'ole
6) Love the way you hold me - Jamie Grace
7) Let it be - The Beatles
8) Under the bridge - Red hot chili peppers
9) Jesus of Suburbia - Green day
10) Four chords - Axis of Awesome - This one lists the rest of the songs not included in my list.
Of course, I couldn't help but write my own ukulele song in tribute of the four chord staple, so here it is.
Okay, you have a starting place. Learn those four chords and then the songs they are in. Don't forget to buy an ukulele. "Liana Soprano Ukulele LU132"
Peace out.