Buying a new Ukulele is  relatively simple these days: Most Ukuleles you will find are of good quality, there are just a few things to watch out for: Ukuleles come in four sizes: The Soprano, The Concert, The Tenor and the Baritone. The Soprano is the one which is the cheapest and therefore the most popular one among starters.
Whey you shop for a Soprano, try not the get the cheapest one as most of these may not sound that pleasing. You only have to pay a little more to find yourself with a better instrument.
The one thing to watch out for is the tuners: Try to find a Ukulele which does have modern type tuners. Modern type tuners look the same as the type of tuners which are found on a Classical guitar. These type of tuners make sure you can actually tune your Ukulele. The traditional type of tuners for the Ukulele tend to slip and will make it hard to tune up correctly. A Ukulele which is not tuned correctly will be not much fun to play and will also make the learning of the instrument a less pleasant experience.

Happy shopping,
Eddie