Some great advice from Artful Codger. Just a few things I'd disagree with. I would forget about the capo and learn to transpose.
I haven't tried the uke thong, but I do find a strap of some kind is necessary. If you are just strumming chords, you might manage without a strap, but for any kind of lead work, you will need it, so you might as well get used to it. I use a braided leather shoe lace for most of my ukes, but my metal bodied reso uke is heavy enough that I use a one inch wide strap.
If you find a uke with an inlay at the 3rd fret that you really like, don't let that extra inlay deter you. I can't even recall which of my ukes and banjoleles have one. The advice about the side dots is good. Some folks hold the instrument so that they can see the fretboard, but some, like me and Artful, need the side dots. These are relatively easy to apply if your uke doesn't come with them. I have applied them to 2 guitars, a banjo and a uke. I merely drilled small holes in the side of the fingerboard and filled them with either white paint (on an unbound board) or a white glue and rosewood dust paste (on a bound board). Charcoal dust could be used in place of rosewood dust or you could use a putty stick of the appropriate colour.
Since I own a number of guitars, banjos and mandolins, I do own a few string winders, but I have never used them on a uke.
I have a few ukes with friction tuners, but I prefer geared tuners.