The tourist season is fast becoming an all-year-round affair in Rome. For touring and good weather sports (such as golf, swimming, etc.) April to late October or early November is the best. For winter sports, December to March.
For women: in spring, summer and autumn, lightweight clothes including cottons for summer and light sweaters (evenings can be cool). Low-heeled shoes for sightseeing.
A cocktail or short evening dress might be useful.
When visiting churches (shorts are forbidden) wear hats or scarves on your head, stockings and preferably dresses with sleeves.
For men: in spring, summer and autumn, lightweight suits, a light topcoat, slacks and sport jackets. Swimming trunks and beach coats. Heavy clothes in winter.
Although Rome is generally regarded as a sunny city, in the winter is a rainy everywhere. But the months from April to November are usually filled with warm sunny days; July and August normally are the hottest months of the year.
See the chart below, indicating maximum and minimum average temperatures in Rome and the cities around in degrees centigrade (oC).