I would recommend staying in Luca's appratement. It was small but suitable for 2 people. It was clean and just next the Forum Romanum with nice view. Most of attractions within walking distance.
Luca recommend us bus which tooks us near his place. What I should recommend is to check bus stop in google street view, because in buses in Rome there is no information about next stop.
We were there in January but Luca provided us electrical heater. We couldn't take it upstairs but it was not cold there.
Some people wrote about problem with hot water, but we had no problem. It was always available. Nothing was missing in appartement for me.