UkeSchool.com is a tool you can use to help you learn ukulele. The most important word in that sentence is "you". You're the one who wants to learn to play the ukulele enough that you found your way here. Good work! In so doing, you've demonstrated at least as much focus and determination as you will need to move forward. Learning the ukulele is easy - so is finding a website - the biggest trick to both is just to actually do it.
The website is designed so that you can learn at your own pace, quickly and easily. That's absolutely critical to re-wiring your brain as effectively as possible. You shouldn't let some pre-ordained 'pace' keep you drilling at something you are ready to move beyond, or push you ahead to things you aren't really ready for. To keep you tuned to your own pace, there are a number of mini virtual jam sessions with the lessons, that will patiently keep plugging away with you until you feel good about how you're doing.
You are encouraged to find a level of comfort while you are playing. Whether it is a simple exercise with only one chord, or a complicated finger-picking run, the goal is to get to the point where you are no longer thinking about, no longer stressing about, no longer even concsiously aware of what you have just learned. The thinking just fades away and all that is left in your heart and mind is music. Or, as Charlie Parker said, "you slave away at your instrument, you learn the scales, the theory...and then you forget everything you ever learned and just play." When you find you're just playing - you're ready to move along - quickly and easily.
You can choose to start at the beginning, and work your way faithfully through all the material at the school in order. Or, you could just browse the site map and pick lessons or anything else to suit your fancy. But either way, you and your ukulele are going to have to spend some time together. How much is up to you. If you only work at it for an hour a week, it will take forever. If you work on it for an hour or two four times a week, you will move swiftly - you could start at labour day and put on nice chrismas shows. If you're fortunate enough to have little better to than learning to play the ukulele, and can throw a few hours at it every day, you'll be able to kick some serious butt within a month. Any more than that, though, and you'll really be biting off more than you can chew - your learing will become less effective. Until you're in awesome form, you'll need the better part of 24 hours to allow the brain re-wiring of a few hours of musical training to settle in and free up space for new stuff.