Precision air pumps are a reliable and a cost effective option.
For hydroponic systems where many air pumps would normally be used, or just when large volumes of air is needed.
These magnetic air pumps by Hailea are very strong and reliable.
The most common air stone used in hydroponics is the 'Golf Ball Airstone'. Roughly 25mm in diameter - the golf ball airstone is suitable for most situations.
A check valve (or non-return valve) should be used whenever an air pump is positioned beside or below a nutrient tank. It will prevent nutrient flowing back into the air pump when it is turned off.