Hi Kris!
The best thing for you to do right now is get a good guidebook and spend some time with it! Advance research is highly advised and very helpful when starting from Square One. It will answer some of your questions and help you ask others here which are more specific. As you've found the RS forum, the RS Rome guidebook will be the logical companion resource.
It'll also be helpful to break your questions - once you've done some reading - into individual posts as trying to cover everything in a single post will eventually result in a very long, unwieldy thread both for you and for us to wade through! Make it easier on yourself, OK? Post by topic: transport, attractions, hotel, etc. Also, provide the exact dates of your trip, including date/location your flying from to the date you fly home.
The good news is the Rome is relatively easy, and settling in for a week with a day trip or two is a great way to get to know the Eternal City. There are umptybumpty things to see and do but you should make your own must-see list first, and then we can help flesh it out a bit, talk advance tickets, etc.
Whether to take tours or not is a personal preference; some people enjoy them and some don't so there's no right or wrong. We haven't had the need for them in Rome (yet) however there's an attraction or two which require them, and there can be specific advantages to booking one for the Vatican Museums.