Chris,
Staying in the immediate area around Termini station would probably be the best idea. That's where you'll most likely be arriving in Rome, and will provide easy access to all modes of transportation as well as the Hop on / Hop off Bus tours. If you need to use Taxi to reach your Hotel, the ride will be short and reasonably cheap.
Given that some of your party have mobility issues, be sure to plan lots of rest breaks in your touring. I've found that while it's easy to walk to many sites in Rome, it can also be VERY tiring!
Happy travels!