Few Renaissance writers, apart from Jonson and Milton read the other three elegist Catullus, Tibullus and Propertius. I think they are worth reading too. Milton was lucky enough to be able to read Greek and so he was also able to read Homer.
Why should we care about the Romans and the Greeks? Because by reading them, we get all the Easter eggs hidden in the texts. By reading them, you can get what Milton was trying to do with his incredibly complicated way of stating things. By reading them, you understand so much more and not just Shakespeare and Ovid. If you can, read them in Latin.
I am thinking of taking Ovid in translation and putting him back into Latin and see how close to his own words I get. That is studying Latin old school. They did it like that in Milton and Shakespeare's day. That is how they got to be so good at it.