What is the best/easiest way to get from the Colosseum to the Catacombs and then from the Catacombs to Vatican Area?
Which catacombs Jason?
The largest selektion of catacombs is out along the Via Appia Antica; is this the area you are asking about? If so you can get there by taking the Metro B at the Colosseum to the Piramide stop and then the city bus (I think it's #118 but check) or the hop on-hop off archeobus from the Colosseum stop (expensive). If you take the city bus remember to validate your ticket, and at some of the catacombs the exit may be far from the entrance.
Which ones? Anyway, if you want to visit St. Agnes' catacombs (which are slightly off the beaten path) take the metro (B line) at "Colosseo"; then, make sure the train's headed to "Conca d'Oro" and take it, getting off at the "Sant'Agnese/Annibaliano" stop (which is located on the "B1" branch of the "B" line); the church and its catacombs are a small walk away. In order to return to the Vatican you can take the metro and get off at "Termini";
then, take the "A" line towards "Battistini" and get off at the "Ottaviano - S. Pietro" stop.