Types of sprouts you can easily grow:

Alfalfa sprouts are perhaps the easiest sprouts to grow at home. They will be ready to migrate to the growing cabinet in about 3 to 4 days.

Radish sprouts are a bit more delicate. The leaves grow larger, and can be inadvertently separated from the root stalk if you handle them too roughly. They will be ready to move to the cabinet a day earlier than the alfalfa sprouts.

Broccoli sprouts are also very easy to propagate. They are very sturdy and can take about as much handling as the alfalfa sprouts. I have heard that they are about twenty times more potent in anti-carcinogenic factors than the grown broccoli vegetable found in stores. They will be ready to move to the cabinet a day or two later than the alfalfa sprouts. 

The tray construction is fairly simple.