Definitely do NOT buy the Omnia pass. I've really never seen that one recommended in this forum, and it would be an considerable waste of money if all you want to see are the Vatican Museums, St. Peter's and the Colosseum/Palatine/Forum. Understand that the pass doesn't cover escorted tours.
ALL pre-ordered tickets or tours from ANY source skip ticket lines. NONE of them skip security-check queues at the Vatican Museums or Colosseum.
I'll go along with the others who've recommended spending the $$ for the "Walks of Italy" tours. While they are not inexpensive, you're going to get a quality, small-group experience with a superior guide. If the price is too high, I'd consider the combo museum/basilica tour offered by the Vatican itself, although the group will be larger.
http://www.museivaticani.va/content/museivaticani/en/visita-i-musei/scegli-la-visita/musei-e-collezioni/musei-vaticani-e-basilica-di-san-pietro/visita-guidata-musei-e-basilica-s--pietro-per-singoli-e-gruppi-.html
I would spend the $$ for a comprehensive tour of the Colosseum/Forum/Palatine as that group can be harder to understand without advance reading or a knowledgeable guide. Walks of Italy, The Roman. Guy, Context and some other tour providers have been favorably reviewed in past forum posts. I'd look into one of these versus what's offered on the coopculture website as I don't believe they provide a guided tour of all three attractions.
Editing to add: Sorry for the redundancy, Gerri! Was posting at the same time you were!