The are also direct trains to Prague, which made for a nice side trip when I needed to go to Leipzig.
They're longer, about 3h I think.
Sadly I can only recommend against that. Because you can't book them together you need to plan in a lengthy stop in case of delays. I made that mistake twice and both times I was badly burned.
There is a train every hour. If you don't buy a discounted ticket, you can take any train you want.
You can also take the bus, which is a lot cheaper but takes longer.