Wow, that is a very vague question... you might get a better response if you provide a little information for us to digest.
What kind of valves? What pressure ranges? what size?
In regards to how many types of valves there are, there are far too many for someone to sit here and list them all out to you, unless you are only after very generic classes.
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Don't believe everything you read on the Internet!
Welcome! This link http://www.engineeringtoolbox.com/control-valves-leakage-d_484.html should answer your question. But in the future, most would expect you to have at least attempted a Google search before posing a basic question. (The link above was the first hit when Googling 'valve leakage class'.)
Selection is easy. There are many simple techniques to select anything. Selecting something to a set of criteria is much harder. You must first have a set of criteria. (You did not provide any criteria.) Then you must understand the meaning of the criteria. Then you examine what parts are available and see if the manufacturer's specifications meet the criteria. If you wish to be sophisticated you can even apply a weighted value to how well a part meets the criteria. This can be helpful later to prove your selection process.
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"A good scientist is a person with original ideas. A good engineer is a person who makes a design that works with as few original ideas as possible. There are no prima donnas in engineering." Freeman Dyson
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