Tuscany trip

It makes sense to have a car, cost wise, with so many people... But you also need to consider what type of lodging you will have, and what you plan to do. With a car you could stay in the Tuscan countryside, and visit other hill towns and wineries. If you are planning to stay in historic city centers and your sight seeing is museums and churches, you are far better off taking the train.

You can't have a car in any of the places you mentioned, at least not inside the city centers. The historical centers are forbidden to non residents' motor vehicle traffic, therefore your rental car would be gathering dust in a parking garage.
10 people probably need 3 vehicles (or two large ones) once luggage is accounted for. If you rent it for a day just to go from Rome to Florence, it will cost you €150 for the rental (3 cars at about €50 each a day) + €60+ per vehicle for gas and tolls. So €350 is a good estimate for 3 cars (not much less for two large cars since they rent for a higher rate).
10 train tickets from Rome to Florence are €450 (€45x10) if you pay full fare, but if you are willing to purchase in advance (they go on sale 120 days prior) and commit to a date and time (discounted tickets aren't changeable or refundable) you can save about 60%, making the train not only the more convenient, but also the cheaper option.

I agree with Roberto. There's a place on the Trenitalia website to book tickets for large groups. With a group of ten, you will be able to fill a small-group tour to a winery or two (if that's your reason for going to Chianti area), so you wouldn't need a car for that, either.

thanks everyone for your kind advice, we will take trains and try to find a tour to Chianti, probably from Florence.

Thanks.

Groups of 10 qualify for a 20% discount on Trenitalia, though this probably can't be combined with advance-purchase discounts. FYI, renting a nine-passenger van costs just as much as renting three cars.