I stayed in an apartment near the Vatican last June. I took the bus anywhere I didn't walk with 2 exceptions. I was torn between a place in Trastevere and Prati, but I read too many comments about the noise at night in Trastevere, so I chose Prati.
I was in Trastevere on a Saturday night for an EatWith dinner with Federica & Barbara, and it easily confirmed that I'd made the right decision. The party ran late, so I got to see the heart of the neighborhood at its rowdiest and busiest time.
You can Google "rome neighborhoods" and find lots of details about them as well as maps. This is just one example.
I was a little confused by "large" neighborhood. I used Google maps to find my way around. You can even get public transport information from it. If I got lost, I invariably learned that things were much closer than I expected. My greatest challenge was the tendency for streets to change names or not be marked at all. So when you come to an intersection, look at all the corners for the street names, including the ones behind you!
I found my apartment using Booking.com. It is La Porta Rossa di Borgo -- Vatican Luxury Suite. There are 2 apartments there. I stayed in the 1 bedroom with the green sofa, the green upholstered seat on the balcony and the lavender bed. The apartment is listed on many other rental sites.