Recommended and mentioned products
Google Play desktop client
Going without Google also means you can't use the Google Play Store from your phone to install apps. You can find good open source alternatives for some things, and F-Droid is highly recommended. To get WhatsApp and your banking app you'll need to use a Play Store downloader. There are a few web-based ones. I use a program called Raccoon. Be aware with all of this that there's an element of trust involved with...
A free-as-in-freedom re-implementation of Google’s proprietary Android user space apps and...
You can choose whether or not to install the Google software package, but as far as I know it's all or nothing. It has to be installed alongside the OS, before first boot, and can't really be reigned in afterwards. Be aware that many apps rely on Google Play Services, and won't work without them. The microG project aims to provide an open-source, privacy friendly implementation. It's incomplete but seems to work...
Operating system for smartphones and tablet computers, based on the Android
There are community supported Android variants, LineageOS is probably a good starting point for your own investigation. My experience on a MotoG7 has been almost flawless, but has experienced an issue requiring a reboot once in a blue moon.