mUNGus Hi there! Thanks for reaching out, and welcome to the GrapheneOS community.
With GrapheneOS, you don't really have to give all that much in terms of compatibility/comfort. While GrapheneOS's focus is security (and by extension, privacy), the development team has put a lot of care in maintaining compatibility as much as possible.
Hardening features that may cause issues with problematic applications (such as those with memory corruption bugs caught by GrapheneOS's hardened_malloc) can be relaxed system-wide or per-app to ensure that you can use them if you wish.
Furthermore, GrapheneOS offers Sandboxed Google Play which means that you can use Google Play Services and Play Store without having to give those apps special privileges as you would on Stock OS. On GrapheneOS, these apps live in the same sandbox as every other app you'd install on your device, and are bound by the same restrictions.
https://grapheneos.org/features#sandboxed-google-play provides more information about the feature.
mUNGus In terms of browsing I was looking into a multiple browser method (bromite or Vanadium and firefox sound promising), even tho Iam not really sure about it and will propably have to test it out when the OS is up and running.
For browsing, here's the official source in the GrapheneOS documentation:
In my personal opinion, Vanadium is just fine for most things. If you want an app with some fingerprinting protections, an ad-blocker and other things like that, I would suggest Brave instead of Bromite, as Bromite tends to fall behind with regards to updates, which can be a big issue and leave you vulnerable.
As per the section linked above, I would discourage the use of Firefox, as it generally lags behind in security compared to Chromium - especially in Android. However, if you want to use it, you can do that just fine on GrapheneOS!
mUNGus Is it generally better to visit websites, with privacy orientated options enabled, than using correspodning apps (e.g. shopping, gas prices, translator, ebay ...)?
For this question, I'll forward you to a thread we had here a few days back that may give you some additional information to help you decide:
Using websites is perfectly fine. Apps have some advantages (they can be more seamless, refined and user-friendly), and they can be perfectly private and secure as well (you get to control what they can access via permissions).
If you can get by with just using your browser; go for it. See how it feels, but don't unnecessarily restrict yourself to the browser. Stick to well-made and modern apps, adjust their permissions to your liking/comfort and take advantage of GrapheneOS's features (such as Storage Scopes) to lessen the impact of apps that ask for permissions they don't really need.
I hope you find this answer helpful!