Rome station left luggage is a lottery. Can be quick, can be very slow, up to an hour to deposit; quicker to pick up assuming it is not lunchtime. If one has about two to three hours to kill between trains here with luggage, this is what to do:

Go through Mokka cafe by platform 24 (where the airport express comes in) onto the street. Cross road into Via Gioberti, pull your luggage 200 metres to Restaurant Tudini on first corner on left side of road. They have good tables outside (best round corner in via F turati) and they are very happy to accommodate your bags by your table. Lunch is good tourist-style menu and they speak English. You can get good wine in a jug. Cost of the meal about 25 euros a head. They also do Prosecco in a bottle, good to start if you fancy fizzy white from the country.

You are also near enough to walk to S. Maria Maggiore, 300 metres further on; it's a spectacularly ornate church.

The metro is really cheap and easy to use. Its worth making use of it rather than trying to get everywhere on foot, as its a big city to get around. Vatican city is especially a little out of the way, so jump on red metro line a and you'll be there in a jiffy!