Amen (& Marco)'s apartment was everything that was described. The short walk from the train station (10 min if you exit from the midway point, 20 min if you exit from the normal exit at the north end onto Via Marsala) is manageable with luggage.
The walk down Via Marsala was a little bit intimidating but once we arrived in the neighborhood of the apartment we felt more comfortable. After some google map work, we chose another route that added 5 min, but we felt more comfortable (follow Via dei Ramni to the left, turn right at Piazza dei Siculi and down Via dei Salentini to Via Tiburtina Antica and up Via Tiburtina to Via dei Latini). I know there are more opportunities to miss a turn, but it's a better neighborhood.
There are plenty of restaurants in the area and once you get to Termini Station you can get to any place along the metro lines easily.
The apartment is very comfortable and has everything that you need for a family stay.