For F-Droid in specific, you'll need an F-Droid client. I use Droid-ify (GitHub) (F-Droid) (IzzyOnDroid), but you can use whichever you prefer. F-Droid is a good source for open source apps.

If you're sideloading from different sources, Obtanium (GitHub) (IzzyOnDroid) is useful to download apps, and keep them updated. You can even kinda use it as an F-Droid client.

Google is pretty lax on what it allows on Google play, so unless you're trying to avoid using Google services or you want to install apps that aren't on the play store, you don't need to do it.

If you want adbocking and extra features in some apps (especially YouTube), check out ReVanced.

Google isn't lying - there are risks to sideloading if you don't know what you're doing. Make sure what you're downloading is coming from legitimate sources you trust. For example, if you look up ReVanced, some unofficial websites show up which may have malware. Triple check everything is coming from an official source.