I frequently get asked for my advice on purchasing a ukulele. And in general, I recommend new musicians start off with an affordable one! But what about when you're ready to upgrade?
I suggest beginners first learn how to play on an inexpensive instrument, then have fun browsing music stores and trying out different makes, models, and sizes. Which one feels good in your hands? Which one has a beautiful tone? What's your budget? Those are all reasonable questions to consider, but there's no rush to upgrade. It's not the instrument that matters, it's what you do with it.
UPDATED 3/21/17: When I initially posted this, I should have gone into more depth on what's probably the biggest factor to consider when you're upgrading your ukulele— the size! The ukulele comes in four sizes and from smallest to largest, they are: soprano (sometimes called "standard"), concert, tenor, and baritone (baritone follows a different tuning, however). There are pros and cons to each, but I think the most important thing to consider is the size of the instrument in relationship to the size of the player. Many players do well with the soprano/standard ukulele, but plenty of others prefer the size of concert of tenor ukes because the longer necks give your fingers more room to shape the chords. It's always best to try the instruments so you can compare what each one feels like.
Want to read more? These links may be helpful as you consider your options:
Ukulele Buying Guide from ukuguides.com
Ukulele Sizes from liveukulele.com