I uploaded my first iOS app today to iTunes Connect. I uploaded it over xCode 7.2.1 and I see the app as "Processing" inside the "activity"-tab. But under "AppStore"-tab for version 1.0 there is no app build visible. I only see the message that I should upload a build with xCode or Application Loader.
Is this normal or should I wait some time that the app is also showing up?
Yes, this is perfectly normal. You just have to wait for it to finish processing (can take a few minutes or a few hours depending on Apple's traffic). Once it is done processing, it will appear in that builds section and you can select it as the version you want to submit. This is the same for TestFlight.
I recommend getting watchbuild and running it on your terminal so you can just get a notification on your computer when your build is done processing instead of having to keep checking App Store Connect.