I have recently bought a ukulele myself, and five months later (with little practicing) I already know enough to play pleasant sounding songs that seem more advanced than they are. It is indeed an easy instrument to learn, and fun to play as well.
The three main types you are referring to are soprano, concert, and tenor ukulele. Sopranos are the smallest, about 21 inches long, and the most common type. They are usually cheaper as well. Their frets are close together, a plus of you have smaller hands or you have trouble reaching for notes. Concert (also called 'alto') ukuleles are larger with a deeper, fuller sound to them. They have more frets than sopranos (usually) and therefore have a larger note range. Tenors are the largest of the three, with an even fuller sound than concert ukuleles. They are good if you have large hands or long fingers, since the frets are more widely-spaced. However, I purchased a tenor ukulele, but it is hard for me to hold correctly because of its size (although I am about a thirteen year old's size). I can only play the tenor ukulele sitting down and resting it against my knee.
Since you mentioned you have small hands, I would recommend the soprano or concert ukulele. Make sure you try both at the store and see which size and sound you like better.
Hope this helps! Have fun learning a great instrument
5 months of ukulele playing