Help me with this please!

Hi everyone, me and my mom want to hike the Austrian alps this year and frankly i need some help figuring it out.
I’ve never hiked mountains so i don’t really know how it works. Do you pay to hike certain trails? If not then do you need to book one hotel for a certain amount of days and go on and back from hikes or could there be more than one hotel so that you can switch when wanting to go somewhere further?
Im sorry if these questions sound stupid(they might be), but i don’t want to burden my mom with fthe research on this.
And if you’ve already got experience which austrian trails are the best?
Thanks in advance, i just need all the help i can get so please don’t shy away from responding.
(Also i live in lower saxony germany and will need to take a train or a couple). Also if some of you know if there are any trains going directly from south germany to the alps then i’d appreciate it.