For me this is an economics question. which is less expensive and less time consuming for you. the drive from Venice to Chianti, if done on the autostrada, is pretty boring. the country is flat and mostly agricultural.
Driving through Tuscany and Umbria is enjoyable and you can see some of the towns along the way. I would chose #2. However, renting a car near the train station is easy but it isn't easy driving out of the centro storico. I prefer to rent at the airport. It can be down but for me it was frightening and I swore I wouldn't do it again. Same for Rome, I won't drive in the city.
As we speak we are departing Bologna for San Marino to drive through the hills of Emilia Romagna and northern Tuscany.