Visit in September vs October and logistics of going to Wolfgangsee

Hi travelers,

I am planning to travel to Vienna, Salzburg, and Prague (3 days each about 10 days) with my friend in 30s and mom in 60s next year. I have some questions:
1. How’s weather like in late August, September, and October? Per quick Google search, the temperature ranges between high 70-80s in late August- early September vs 50-60s in October.
Which month did you go to Austria and when would you recommend going around fall season?

1. I would like to enjoy the calm nature near the lake in St. Wolfgangsee in the Saltzkammergut area and check out the Schafbergbahn cog railway (which looks more appealing than instagram-famous Hallstatt). Would you recommend choosing Salzburg as a base and do a day travel (to avoid dragging luggages in bus and ferry) or stay in St Gilgen or Bad Ischl to enjoy the nature? If latter, did you find it difficult to travel around when using public transportation only?

Thanks in advance!