welcome back to madridman.
I do the metro/bus at minimum as most of the time with a car or walk. However, having lived in the city and visiting now at least once a year, the public transport is very good. The site for trips in English is herehttps://www.metromadrid.es/en/viaja_en_metro/trayecto_recomendado/index.html
For the tickets if staying in Madrid proper the metrobus is ok; for the other trips you mentioned you need separate ticket as such. However, take a look at the Tourist Card; this allows trips in Cercanias suburbian trains either in zone A within Madrid proper or Zone T on the whole cercanias network, again for Cercedilla good to take the C2 from Chamartin, for Avila, Toledo, Segovia you need a separate ticket and train, and for me going to Segovia on the Sepulvedana bus line is better than the train as it leaves you closer to the city center.
For the train to Avila, Toledo, Segovia use the RENFE travel trip journeyhttp://www.renfe.com/EN/viajeros/
La Sepulvedana bushttps://www.lasepulvedana.es/indexcentro.php?lang=en
hope it helps