The climate in Rome, Italy in late March and early April.
There are several airports in Rome. Which one are you going to? I haven't been on public transport, so I don't know much about the details. However, if it is fiumicino, that is, Leonardo da Vinci, there seems to be a train. You look for treno per roma at the airport, and then go to termini, the terminal in the city center. Is the Venice Square Hotel where you are staying in Venice Square? If so, it's close to termini. There are many buses that are the starting stations. Stop at Venice Square, but to be honest, you must have a big bag and a small bag. It's no trouble to get off the plane, take the train or take the bus. You don't know it when you get off the bus. I suggest you find a taxi at the railway station. It's close anyway, so don't save money for convenience.
I've never taken a taxi either. 20 euros should be enough.