Land at Fiuminico Airport and take taxi to accommodation.  48 Euros set fare for everything (for a destination within the Aurelian Walls).  A good way of getting to your accommodation without any fuss to start with.  Then you can collapse and recover from the journey.

Buy Roma passes for three days - free access to the first two sites and discounts on all others covered by the pass - use it for Colosseum combo and the Borghese gallery - and jump the long queues as well.  Brilliant.  Free transport on buses and metro as well means you can get anywhere in central Rome for free.  Walking is required but you will get a good flavour of the local area.  Vatican tours are there and it is worth it. Suggest you could do St. Peter's Square first, then the Basilica, as they are free and access anytime.  Get a good guide book and the free podcast tours onto your ipod or MP player.  They tell you everything the tours do.  Then book a tour for the Vatican Museums BUT before you leave the Sistine Chapel say you want to break off the tour and hand back the headset.  That will leave you free to wander the museums for how ever long you want and to spend more time in the Chapel.  Take lunch, or tea, with you.  You could easily spend a whole day in the museums.  You can also go up into the dome of St Peter's (extra charge).

Other places to visit - Trevi fountain, Colosseum, Pantheon, various piazzas, Quirinale, Roman Forum and Palatine Hill, Piazza Venezia, Piazza Navona, Castel Saint Angelo.  There are lots of other places you could visit but suggest those are the main ones.

Food is variable and pretty cheap...pasta is good, pizzas are staple fare.  Suggest that you look for restaurants that are frequented by locals and not ones that are empty....there is usually a reason they are empty.

Try and get to see an opera....even if you don't fancy are in Rome!