Here's my thoughts on the Mayans. I played them exclusively for my first year of civing. They are so powerful that they allow you to win easily on low levels without learning the art of micro-managing (MM) (which you will need on higher levels). My advice to newbs is to NOT play Mayans or Sumeria until you've learned to properly manage your cities, otherwise you will spend your first half dozen emperor-level games getting your ars handed to you.
If I could do it all over again, I'd begin playing with 'sucky' civs that would force me to learn good city mgt. I'd also toy around with gov't other than Republic or Monarchy (which you will ultimately end up playing - via experience).
I'm now winning my first 'true' DG game with my first attempt with Sumeria. Although I'm happy I can win at this level, I think my next game will be with a 'sucky' civ at Monarch level - probably going the communism route - just to have a different kind of experience.