You can buy a regular phone that has an active community on XDA forums and flash a ROM without installing google services afterwards.

If you can't do that, some phones just let you disable google services. On others you can try getting root access and then disabling them.

As an alternative (or addition for closed-source apps) to F-Droid I can recommend APKUpdater. It is highly configurable, has multiple apk sources, has search and can install apps from Google Play Store.