The first is correct and not too bad. The second is incorrect. He has a lot of pop and rock albums. (That they are ‘music’ is understood) He has a lot of albums in the pop and rock genre(s). (If you think of pop and rock as different genres, then you need the ‘s’. But sometimes people might lump together pop and soft rock, in which case it’s just one genre. ‘style’ is less precise because these are well-known music categories. You’d use ‘style’ to describe something that doesn’t have a clear definition. )

It is usually (gramatically) correct in English to say the _____ of ______, but it is also usually preferred to say things as adjective + noun. Often, phrases in the former style would sound awkward in English, but here both sentences sound pretty good. The first sentence still sounds slightly better (There are rarer occasions where ______ of ______ sounds better). Since pop and rock are both styles, you might say: pop and rock style music. For whatever reason, the addition of the word "style" makes this sound more natural than it would if it was just: He has a lot of albums of pop and rock. That would sound weird, but this sounds good.

The first one is more correct!