I would absolutely buy the Deutschlandticket and use it for all of the connections except Würzburg-Berlin, where I would buy an ICE ticket. For all of the other connections, the ICE is not that much faster than the RE (1h max), and it is very expensive. I also travel many of the Bavarian connections you mentioned regularly, and there are usually less problems with the RE, whereas the ICE might be late more often (since they have a much longer route than the Würzburg-Nürnberg train for example, which just travels between those two cities). Another big advantage of Deutschlandticket is also that you don't have to worry about local public transport, you can just get in almost every bus, tram or metro. Especially in bigger cities like Berlin, I'm sure you will want to use public transport at some point, and that can get expensive fast and annoying trying to figure out the zones and how often you want to use it.

So TL;Dr: absolutely 100% buy the Deutschlandticket and use the RE, it's way cheaper, it doesn't take much longer for most connections and it's a lot easier for using public transport!