First things first, if you want to become a ukulele maestro, you need a Ukulele. If you already have a uke, that's great! skip to the next step!
You will want a cheap ukulele, because until you can play really well you do not deserve a master piece. Once you have stuck with it for several months and can play more than 6 chords and a few songs, then you can look into a newer more expensive Ukuleles.
Whilst you will want a cheap one, you do not want to go too cheap, and get one that can not keep its tune, or sounds like crap. The best method for making sure you get a good quality cheap one is to get one with a brand name that is around a lot of places. Things like Mahalo, Makala, Kala, Stagg, Lanakai, etc.
Ukuleles come in a range of sizes, Soprano is the smallest and the 'usual' one that is seen in movies, shows or other. More often people are using the next size up 'Concert', or even the larger one 'Tenor' because they are easier for larger hands. I personally use a Tenor because it has more ring and sound to it, but I can play a Soprano just as easily as they are tuned the same.
A Baritone Ukulele is really a half sized guitar, but its missing the top 2 strings. Good idea if you already play guitar, however it has a fairly different sound and tuning to a regular Ukulele.
My first ukulele after much research cost $50NZD (about $30USD) , and was a Makala Dolphin. It had one of the better sounds for the cheaper ones, despite the nasty dolphin bridge.
The only thing needed to make these ukuleles sound far better is a set of Aquila strings, which are also softer than the ones that come with it. The softness and better sound is something you really appreciate once you have been playing for a day or two.
Next -> Step 2 - Getting to know your Ukulele