I can help with information about Mexico... I live in Puebla, Mexico. Close to Mexico City... I travel frequently to Mexico City, only business because there are better places for vacations in Mexico.
I have been in all touristic locations in Mexico, and others not so. I'm not listed as a travel helper, just sign in today to this site.
About the security in Mexico City, yes, you have to be careful, as much as other big cities like Atlanta, is not as bad as you see in the news. Anyway, I don't recommend spending more thant 4 or 5 days in Mexico City, much better places around to see.
Transportation is not a problem, very reliable (no snow storms and closing airports). Depending on how far you are going, bus is always a good option. They are even better than in the states, probably because a lot of people travel by bus because of the high cost of flying (fare to Houston is cheaper than CanCun).
Everything depends on what kind of trip you want. sunny beaches, hiking in the mountains, cultural and archeological trip, adventure trip with rappel wild rivers, etc... is a big country and a month is not that long.
Want some pictures of Mexico, photography is my Hobby. I'll post later a site where my pictures are. Need more specific advice... I'll be checking responses to this post.