We spent a week in Rome with our two teenage kids, and had a wonderful time in Paolo's apartment. It is every bit as nice as in the photos (even a bit nicer), bright and atmospheric - a place to feel at home during your vacation. It has all you need, and the kitchen is well-equipped if you want to cook. Testaccio market has excellent groceries and a good plate of pasta, Eataly is more touristy and upmarket, but worth a visit for the gigantic selection of Italian delicacies.
The location of the apartment is great, and it's fairly quiet. You can get to all the sights by bus or metro or even walking, but you are away from the crowds.
Paolo is a really lovely host who welcomed us personally and gave us lots of tips and help - thanks for the warm hospitality!