A simple guide to help you choose your new drum!
SizeThe larger your drum, the deeper its voice. The 12" drum is a good choice for a drum which is easy to travel with, versatile, lightweight, and comfortable to play. The 16" drums do have a much deeper sound, they are very nice if you're looking for a more sonorous voice from your hand drum. The 20" drums can have a very deep sound and are louder and more resonant than the smaller drums, but are more difficult to carry with you since they are quite large.
There is really no difference between the tambourine style drums or round drums (single-sided) when it comes to sound or playability, it is mostly a matter of aesthetics and which look you prefer. The Sioux-style drums are absolutely gorgeous (with thick wood frames visible) but aren't quite as comfortable to play since they have one handle on the top. You can rest them on your leg to play when sitting or hold with one hand a bit away from yourself and play them that way. Usually people choose that style if they want a beautiful display drum to hang on a wall and to play more occasionally, though they are certainly playable and wonderful drums.
If you want a lighter weight, deeper drum that is very comfortable to carry I would go with the single-sided hand drum, if you want a much more substantial drum that is going to be a bit heavier and would be appropriate for using in a sweat lodge or in high humidity (since it has a much thicker hide it can be 'tuned' by small applications of ambient heat/humidity) the Sioux-style double-sided drums might be a better choice for you.