Hello TravelCouple,
Your post makes it sound like you're looking at doing all three of these in a day which I think is too ambitious. If these are separate trips you're planning then I would say a day for Siena and day trip to San Gimignano and winery on another day seems reasonable.
Siena is the classic day trip from Florence and is easily achievable via either bus or train. Most people opt for the bus since it drops you in town rather than at the far edge of city. Siena is city of 50K and can easily occupy and entire day of exploration all by itself before heading back to Florence on the last bus/train.
One of the reasons it is the classic day is other smaller towns - like San Gimignano - are harder to reach with public transportation. SG has no train station so at least the last part of the trip needs to be completed by car or bus, There are buses that run from Siena to SG (bus 130) but I think a day spent on the bus to Siena, a few hours there, another bus to SG and few hours there before busing back to Florence sounds like a long day of transportation with less mellow Tuscan hilltown experience than I would want.
There is a good page on the transportation options here:
https://www.discovertuscany.com/san-gimignano/how-to-reach-san-gimignano.html
Also people mention tours for wineries because they are often not served by any form of public transportation and the tolerance for drinking and driving in Europe is very, very low so driving yourself is a very bad idea. I know there are definitely winery tour options from Siena and would image from SG as well since it is very touristy.
If you're looking for the wine experience rather than the winery both towns have tasting rooms and offer multiple option for trying wines. (FYI SG specializes in a white wine from a grape called vernaccia which I really like despite being a red wine drinker.) RS lists several wine and/or food tasting options in his writings about Siena.
This is one that also offer tour options - including SG - but there are others as well: https://www.tuscanwineschool.com/savor-siena-food-wine-tour
The Tuscan countryside is as beautiful as advertised but is harder to experience as a tourist with limited time than most of us would like. Be sure to allow yourself time to experience the slow pace of life which is part of the charm.
Have a great trip,
=Tod