I just double-checked and want to correct the info I gave above as well as add more details:
I confirm that the Torre del Mangia tower ticket CANNOT be reserved ahead of time, it has to be bought there. Cost is 8 euro. Kids under 6 can climb up free, but of course need to be with an adult (up to 14 years old have to be with adult).
The Combo ticket Torre del Mangia+Civic Museum is 13 euro and HAS to be purchased at the ticket office for the TOWER, it isn't offered at the museum's ticket office (who knows why?).
The ticket office for the Civic Museum instead offered other combo tickets, in case you're interested in visiting other museums in Siena.
There is combo tickets for:
1. City Museums - for Civic Museum and Santa Maria della Scala - Euro 11.00 and valid for 2 days
2. Winter Pass called "Siena Itinerari d'arte invernale": Euro 14.00 and includes the Civic Museum, Santa Maria della Scala, the Museum dell'Opera and Baptistery of San Giovanni - it is valid 7 days
3. Summer Pass called "Siena Itinerari d'arte estivo": Euro 17.00 and in addition to the museums listed for the Winter pass, also includes the churches of Sant'Agostino and San Bernardino - the pass is valid 7 days
If you're in Siena for several days, the passes are definitely worth considering!