How to avoid getting the pizza all watery?
There are a number of factors that can contribute to a watery pizza:


Cheese If you think the cheese is the culprit, you can try using a "low moisture" mozzarella (these are dry to the touch on the outside).  If you are using a "fresh" mozzarella (these usually are sold in a brine), e.g., classic mozzarella di bufala or mozzarella fior di latte, I recommend slicing the cheese as opposed to grating the cheese.  The idea is that slicing the cheese will produce less surface area, and thereby reduce the amount of water that leeches out.  Also, I recommend dabbing the cheese slices with a kitchen towel to remove any surface moisture.  If you use this method, it will also help to cut the cheese in very thin slices, since that will release more moisture before it touches the pizza and it will also reduce the amount of cooking time.
Tomato Sauce I recommend making the sauce yourself.  As opposed to simmering the tomatoes/sauce on the stove for a long time, I prefer making a light tomato sauce that actually cooks on the pizza itself.  I quickly purée the tomatoes (canned are fine) in a food processor and then let them strain in a fine mesh colander for 30 to 45 minutes, stirring occasionally.  That gets rid of a lot of water (the tomatoes lose about half of their volume).  Throw in some minced garlic, chopped basil, and season and it is ready to go on the pizza.
The Cooking Method Since my home oven doesn't get as hot as a traditional pizza oven, I always "blind" cook my pizza without the cheese.  In other words, I throw the dough, add the sauce, and then cook it with just the sauce for 4 or 5 minutes.  This allows any extra moisture in the sauce to cook off.  I then remove the pizza, add the cheese, and then broil it until the cheese is melted and browned.
The Dough If the dough ends up becoming soggy, you can always compensate by making it a bit thicker.