As mentioned, you are a bit late to get the best advance purchase ticket prices, but browse the Bahn site, you might still find some discounted tickets. Sometimes one train will sell out all of it's discounted tickets while another one, for an early train, or on a different route, will still have those tickets available.
For instance, I can see a Super-Saver fare of 19,90€ for a 7:15 ICE train from Stuttgart on the 1st of November.
These tickets will save you some money, but you must be able to commit to a specific train (time and date) or the non-refundable ticket is worthless.
I wouldn't use regional trains to/from Berlin, but for Stuttgart to Munich, if you are willing to take an extra couple of hours, you can use regional trains with a Quer-durchs-Land-Ticket, a regional pass for any and all regional trains that day (after 9 AM workdays) for 44€.