Here's a big list of custom ROM projects:
https://en.wikipedia.org/wiki/List_of_custom_Android_firmwaresYou'll have to find if they're compatible with your phone though.
As for customization, I highly recommend one that supports the Xposed Framework, which lets you customize parts of the OS which would have previously been impossible without modifying the source code and rebuilding it.
No custom ROM out there comes pre-installed with Google Play services because of legal reasons. If you want them, you can install them separately, but they aren't totally necessary.
maybe with access to some community-driven app repository?
And with that...well, you'll have to look around. You don't need a custom ROM to use a "community-driven app respository". Android isn't a walled garden like iOS, you can just install a separate app store like a regular application without rooting or modifying the OS. There are a lot of alternatives to Google Play out there, so you'll just need to find the one(s) you like most.
Here's a nice list I found:
http://joyofandroid.com/android-app-store-alternatives/
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