Bus from Mexico City

We are thinking of taking a different approach on our Zihua trip next year and flying into Mexico City to take in some of sites and history,checking out Teotihuacan. Then heading to Morelia then to Patzcuaro then heading to Zihua for our annual winter relaxation.
Has anyone done this trip before? We have never took the bus in Mexico and are looking for any advice anyone can offer. Or recommendations anyone has for these other cities.
Thanks