I've been running Android for maybe 2 years without Gapps or a Google account, and like the experience, but I'd also like to do it better because some apps I used to use, now don't run without some Google services. I researched NoGapps but don't quite understand the information well enough, and the different packages available, to know what I need.
It looks like these are packages that simulate the Google play store and main services APIs but return either null data, minimal responses, or data from other open source providers? But I can't find a clear explanation what options there are, and the main differences between them, to help me choose what to install.
My current phone is lineage 14.1 + SuperSU 2.79 on a Samsung S7 G930F, and I don't use the Play Store (I use FDroid and sideloading).
Just to clarify (following @Izzy's excellent "basics" reply so far), the main issue thinking about it isn't so much "which of these packages can I use to replace a Google library".
The real issue is, to what extent do these No Gapps alternatives meet the presumed goal of allowing software to still work (by faking a playstore/location provider/other service that they expect GApps to have provided), but also in reality sanitising or avoiding actually using Google for these, or reducing and making clear what data is sent to Google if it's used.
So for example, Fakestore sends nothing to Google, period, its job is to fake that Google Play Store is installed and its Android API working, but unfortunately unreachable/empty. But for the rest, it's really hard to know what's still sent and what's sanitised or not sent. If all there is, is a FOSS reimplementation of a Google Library, same data, same auth, mostly same logging/datamining, that's a bit weak and unfortunate, even if unavoidable. If Nlp can fully avoid Google and use more trustworthy sources, that's better. But this is the kind of information and discussion I can't find details about.
I'm realistic here - a person who wants an app that needs Google Push Notifications, has to either fake that functionality as installed but not responsive, or use code that cleans the data and does data leak avoidance as best possible, or must accept they can't use that app. But the information needed for that decision is clarity as to what these NoGapps softwares can do, to minimise or avoid data leaks, and how far they can go to distangling from Google.
That's pretty central to "why I want to use them". I'd like to be clearer what their compromises are and what's possible or not, in terms of data and info passed to Google, and I'm not, which is all that stops me enjoying them ATM.