What was the type of literature encouraged by the renaissance period type of literature?

The Rennaissance, or "Age of Enlightenment", did not encourage a specific type of literature, however one of the most important aspects of the most reknowned writers of the time is that they were largely Humanists.

Poetry, letters, narratives,plays and essays were all popular forms of writing. The novel, as we know it, did not exist, perhaps the closes you can get to a novel from that era is Thomas More's Utopia, a two-part philosophical narrative which is mainly concerned with freedom of religion (More was a Catholic in England around the time Henry VIII formed the protestant Church of England, he was eventually executed for refusing to denounce his faith).

Much of the humanist writing of this time was concerened with religion, corruption of rulers (read More's Utopia, Erasmus' The Praise of Folly, Shakespeare's King Lear, and Measure for Measure, Donne's Satyres).

Largely there was also a huge movement that focussed on classical writings that had, hiterto, been ignored throughout the 'Dark Ages'. There was a revival of interest in the writings of Herodotus, Homer, Virgil, Cicero etc...

Alongside that there is much literature about discoveries, both geographic and scientific (Shakespeare's The Tempest, Nashe's The Unfortunate Traveller etc...)

There were many other writings, I would particulalry reccommend reading the poetry, essays and sermons of John Donne, see how he includes science and discovery, satire, classical poetic forms, criticism, crisis of faith and sex. Incidentally he was distantly related to Thomas More, but renounced his Catholicism at the behest of James I and became a Protestant priest.