I understand it looks scary at first, and you're good to always be careful with new apps. Aurora Store only needs what's absolutely necessary for all it's functions to work, and it is open source, actively maintained and used by a lot of people, which are all good signs to look for in a new app.
For me it runs perfectly well with just internet access, storage scopes (no files but the ones it creates), notifications and permission to install apps. The full storage access is probably needed to install some games that use different folders, but I'm not sure about that. The default settings for every step of the first setup should work well for you. Let us know if you have any specific questions.
Btw Play Store needs those permissions as well and has many more by default on stock android. The main difference is now you are in charge, so you get to see behind the curtain and it looks scary at first. :)