Given the timing of Rome's UU; (it's going to be difficult to get offensive units to take out Rome before they can build Legions), the best things if Rome is a neighbor will be:
1. Do whatever it is that Rome's historical agenda wants you to do.
2. Avoid forward settling towards Rome
3. Build Walls in cities nearest to Rome so you have bombard; and later on an encampment in them.
Have you seen how buffed up Defender of the faith is? +10 near friendly cities, I think. Might be key on high difficulties. Spearman spam could stop the Legions.