While the taxi idea has merit I would not support the idea of grabbing at taxi at Termini for a guided tour. First, guides in Rome must be licensed so while the driver may be able to drive around and point out a few things he is not going to be a good guide. However, hiring a licenses guide/driver for an hour or two would be a good idea. Solves the luggage problem.
One issue that we had indirectly address with you is that you will be slower and probably much slower than you anticipate. It is function of just not knowing what to do and when. I can walk off a train at Termini and with no thought hit the stairs to the Metro, drop a few coins in the ticket machine, find the platform and be at the Colosseum in 15 minutes. For you, it probably will take 30 minutes or more. You get off the train, where is the metro? someone said go left, find the sign pointing to the metro, there are the stairs, how do I work the ticket machine, read directions, fumble for coins, slowly put in coins and fumble for tickets, now what?, where is the correct platform, am I headed in the right direction?, maybe ask someone, opps, just missed the train, finally get to the Colosseum stop, walk out, now what? And so it goes ! You are just naturally slower. So you really need to factors all of this in your time frame. And that didn't including handling your luggage.
Hiring a private car/driver makes a lot of sense even through it will be expensive.