Advance purchae train tix for Toledo and Segovia?

It is your choice whether you want the peace of mind of having your preferred journey times by purchasing in advance. With the number of journeys a day you are sure to be on one of them.
There will certainly be no discount to or from Toledo at any time, on line or not, and I doubt for Segovia, however surely look for yourself, but I doubt with only three odd weeks to go.

There is no discount for either trip. They are essentially commuter rail type service. I would recommend purchasing tickets once you arrive in Madrid, a day or so before your trips. The lines at Atocha and Charmatin can be very long - 90 minutes or more during peak times. Buy both trips at the same time and get your roundtrip tickets then too. That way you only stand in line once.

I can't speak about Segovia, but I can tell you about Toledo. There are not as many trains as you would think and they do sell out. We strolled into the Atocha station thinking that we could just buy a ticket and get on. But the train we wanted was sold out and there was not another one for over 2 hours. We had to cool our heels at the nearby Museum of Anthropology. Moral of the story is that I would buy the tickets at least a day in advance at the station.

I haven't been to Toledo or Segovia since 1995, before the current trains. But a few years ago, my friend ended up taking the bus to Toledo, because, like Brad, the train he wanted was sold out. He said the bus was fine. So, that's another option.