Teo,
You've received lots of good advice so far. I have a few thoughts to add.....
- I assume your end destination is Bahnhof Zoo as you're staying at a hotel in that area?
- It would help if you could clarify your date. Are you using the European date method of DD.MM.YYYY and travelling on 9 June?
- The train from Munich to Berlin Hbf will be a high speed ICE version, which looks like this - https://goo.gl/images/G3mezs . The trip from Berlin Hbf to Bahnhof Zoo will be via S-Bahn, which looks something like THIS.
I can't provide any details on the different fares, as I'm not as familiar with fares in Germany, and that's already been covered well by the experts here.
If I were making that trip, I'd probably use the train departing Münich at 09:54, arriving Berlin Hbf at 14:24 and Bahnhof Zoo at 14:40. They currently show Saver Fares at 59.90€ for that train, which seems like a good price. You might have noted that the ICE arrival at Berlin Hbf is shown as "tief". As I recall, that means the train is arriving at the lowest level of the station, so you'll have to use the escalators or lifts to get up to the top level where the S-Bahn departs from. It sounds a bit complicated but it's actually very easy.
One other point to note is that you could also purchase tickets for trains in Germany at https://www.trainline.eu/, which sells tickets at the same price as the rail networks. Registration on the website is required, including payment information, but after that the process is very user friendly. One advantage of using Trainline is that they sell tickets for rail networks in several countries in Europe (France, Italy, Spain, etc.), so it's a good website for "one stop shopping", should you be traveling to other countries.