Hey there! I absolutely love Firewatch, Life is Strange was a great experience and I'm about to play Night In The Woods so I commend you for your video game preferences :)
When it comes to the music creation software, I think Reaper might be your best bet seeing as it's very cheap for personal use (60$) and its trial version has full functionality, which is something very rare for DAW (Digital Audio Workstation) software. FL Studio is also great if you want to create music using virtual instruments and samples but the demo version is somewhat limited. Also, while Garage Band isn't commonly considered a professional grade DAW it's actually really capable piece of software, that should be enough for you basic game dev needs and it's probably the most user friendly option available (opening something like Reaper or even FL Studio for the first time might be really overwhelming). Oh and there's of course Logic Pro which is pretty much the industry standard option for mac users. If you're just starting out, there's no need to go for anything other than Garage Band and the basic skills you'll learn using it (working with virtual instruments, recording, working with tracks, basic song arrangement and mixing) will transfer to the next, more 'professional' DAW you decide to use. Garage Band might not be a powerhouse workstation but it's not a toy either, it's a capable piece of software and a great place to start your music journey (perhaps even the best one seeing how user friendly it is). Plus, Garage Band is a bit similar to Logic Pro so it sets you up on a natural upgrade path to the professional quality software.
I have no idea why I'm pimping Garage Band so hard btw, I don't even like Apple...
Going back to the game dev aspect of things, I'm not experienced enough to know this for sure but rhythm game sounds a bit ambitious for your first project. Marrying the bpm of the song with frames displayed on screen might prove... tricky. In any case, I'm excited to see what you'll manage to create and I wish you good luck :)