If you're talking about an object in general, you can generally use either the plural form or the singular form. Some people will say the singular form sounds more formal, although in my view they're basically interchangeable. For example:
Two varieties of apple/apples.
Four types of wood ('wood' is both the singular and plural form)
Several breeds of dog/dogs.
For your last example, you can't really have two types/varieties of an (one) object, unless it is some sort of altered clone, so leave out the article.