Is it possible to upgrade an iPhone 5s on ios 7.0 to the final ios 7 version or ios 8. I am trying to avoid ios 9 as its plagued with a bunch of issues.
Nope, not possible.
You can reset your iPhone directly on the phone, preserving the installed OS version or you can update to the latest version for your device via iTunes.
If you want to update, you can only go to the latest version available, that's iOS 9.2 for the 5S.