I just double checked, and IMO, your fastest route is the high speed train from Naples to Rome Termini and then bus from Rome Tibertina (right next to the train station) to Siena. Florence is well north of Siena. Also the advantage of the bus into Siena is that you will not have to find a way up the hill from the train station. There could be a city bus from the train station or obviously a taxi, but that adds time and cost. If you are staying in the older town area of Siena, your best best would be a bus to Plaza Gramsci.
When I planned and budgeted my trip to Italy. I experimented with the train routes and looked at prices day of, week in advance and a couple months out. It turned out to provide excellent estimates. I also found that the Trenitalia website was extremely easy to use. I had no problems with routes or purchases with my credit card. That surprised me because in other countries I had resorted to Loco2 (which now is merged into RailEurope and I wouldn't use) or trainline.
Also, FYI, the Naples train station can be overwhelming and has a bit of a bad reputation. Never having used this train station made us nervous, and I'm not sure its particularly well signed. We were glad we had given ourselves extra time and we found the there were plenty of helpful train and station employees.
In terms of searches on the forum, I would agree that for whatever reason, they are cumbersome and often I can't find a particular thread that I know had good info. I have been reasonably successful doing searches on BING or google. Often what I'll do is type "Rick Steves" " advance train tickets" and add maybe the name of a person that I recall participated in the thread.
I agree that sometimes responses on the forum can feel brutal. I have on occasion provided a response and then have added that I believe there had been recent threads on the topic. This is not to admonish the OP, but to provide extra into. Sometimes, it can be very hard to discern intent/tone in internet "conversations". Also, I think well experienced travelers might forget how it felt to be a new traveler. Or that some OPs are well seasoned travelers, just new to a particular country or area.