Visiting Italy soon, asking for advice! (Rome)

Hi everyone!

I'm planning a trip to Rome soon and would love some advice from those who live there.

When would it be the best time to go? Should I avoid winter? I'm flexible.

Do you know any cooking school you can recommend? Surely I'll try some eatwith.com event...

Places to see and places to avoid? Love old markets, cosy tea houses, homey restaurants, temples, parks... Slow food restaurant recommendations welcome!

Grazie mille!