I can doubtlessly recommend Rita's Fantasie di Trastevere. The apartment was perfectly clean, brightly decorated, and well-equipped. Located in the heart of Trastevere, in a stunning, quite literally "herb-covered" building, the white interior and the big windows make the flat look even more spacious than it already is. You will find everything you might need here - from an iron and an umbrella to a free bag of top-notch Italian pasta! Right from the reception, which was very pleasant and informative, Rita has been incredibly helpful. I left some belongings of mine in a cab she had recommended and she kindly took the time to meet the driver and send them back to me, which makes her stand out as an honest and reliable host. I believe it is my duty to note that Trastevere (and especially the part where this lovely property is located) can by no means be called "quiet" - it's all about the nightlife. It didn't actually bother us and probably won't be an issue for most people, just FYI.
So, overall our stay at Rita's place was supremely enjoyable and I recommend it to everyone who wants to experience Rome as it is. Rome has no actual city-center, and to my mind, Trastevere is the best possible location to live in in the "eternal city". There aren't many tourists yet everything is at a hand's reach.
Sara, thank you for the 5-star experience! Good luck!
P.S. Mind the low ceiling in the bedroom!