My sister and I just traveled this route a couple of weeks ago. We traveled 1st class as we always do when traveling with luggage.
As the others have answered your questions, I’ll just add this warning from my trip report about the Prague train station so you’re aware:
We ran into a scammer at the Prague train station. They don’t post the train platform number ahead of time, so you have to stand watching the boards. Some guy approached me and told me platform number 5, even though he didn’t know what train I was waiting for or where I was going. Then he offered to take our luggage for us so we wouldn’t have to walk up 35 stairs. Thanks buddy, we’ll take the escalator.
https://community.ricksteves.com/travel-forum/trip-reports/sisters-in-vienna-and-prague-our-trip-report