I would recommend you stay in Emanuela and Celeste's home, it's in a good location and a good price. You can reach the coliseum in around 20-25 minutes walking, depending on your route. The Ponte Lungo metro is around a 15 minute walk, this goes straight to Termini station where you can transfer to another metro on the same ticket. Also, Tuscolana train station 10 minutes away.
The room was clean and also the bathroom regularly cleaned, I had some trepidation about using a shared bathroom but it was always clean and tidy
The house felt very secure and possessions felt safe, you have 3 locked doors to reach your room and the window is off the ground has security bars, so it felt safer than staying in a hotel personally
Overall I'd say this is a great place to stay for a young couple or solo traveller, there is also a great cheap supermarket on your street which is great value.