Before you purchase any tickets, have you looked into the Roma Pass? 25 euro will get you free admission to the Colosseum/Forum/Palentine (one ticket) and the Borghese Gallery, plus a 3-day unlimited metro/bus pass.
Ron in Rome has good advice on the Roma Pass, and it unfortunately looks like they have changed it so that the transportation and site admissions must be used during the same 3 day period. However, given your travel plans this is hopefully not a problem.
You can buy the Roma Pass online, but it is just as easy/effective to buy it when you arrive in Rome. For the Colosseum, you avoid the ticket lines by staying to the LEFT and going straight to the security checkpoint.
For the Borghese Gallery--you will still need to make a reservation in advance. The easiest way to do this is to ask your hotel to do it for you. If that's not an option, the Borghese has a call-back system. Again, Ron in Rome has more information on how to do that. You cannot reserve online and use the Roma Pass as far as I know.