We always recommend starting with Belo Horizonte or Diamantina and leaving Rio and Paraty (read "beaches") for the end of the trip, taking a few days to relax by the sea. But which of these routes is more interesting?
In terms of scenery, descending to Paraty from Cunha, in São Paulo, is the most beautiful route. The park road that cuts through the Bocaina Hills National Park offers breathtaking views of the Atlantic Forest-covered hills. On a clear day, you can see the ocean, and the descent ends right in Paraty.
On the other hand, the descent through Petropolis is not as picturesque and ends on the Washington Luiz Highway, a rather dull freeway. However, this route allows you to visit one of Brazil's most sensational museums, the Imperial Museum of Petropolis.
Now, you can always reach one and go on to the other! Those who descend to Paraty can then come to Rio via the Rio-Santos Highway, another worthwhile road to travel.