Eucryphia's Cave

Typing this from Graphene now, in fact. But, both of those take the Android Open Source Project, without all the bloatware--and largely de-Google the whole thing. They give you much more control over privacy and what the apps you choose to install can do and access on your phone.

I know Graphene sandboxes everything, including the optionally installed Google Play Services which a lot of apps unfortunately require to run. (Lineage uses an alternative to Play Services instead.) So, you can install what would normally be unacceptably intrusive apps and just lock them away from pulling any funny shit with your data, or phoning home. Including the couple of Google things I do still keep around.

I also prefer running much more transparent, privacy-respecting open source apps where possible. Besides the transparency, I'd rather avoid the shitty tech corps entirely where I can. There are pretty good alternatives available for a lot of the usual suspects.

An alternative app store: