I've played many easy fingerstyle versions of "Amazing Grace" on the ukulele, but at the moment this is my favorite. The tab is available for free in the Solo Ukulele ebook by Wlfried Welti . This is a good first fingerstyle solo for beginners.
Tip: On your left hand, your index finger doesn't move much from the first fret, 2nd string (F) so you can keep it anchored there for most of the song. You can see this in the video of Welti playing the song.
Playing fingerstyle ukulele, with information about the songs and where to find the ukulele tablature so that you can play these songs yourself.