AFAIK, there's two types of "secure" when it comes to Android:
- Secure against your phone getting stolen
- Secure against Google's data harvesting
(I guess a third "secure" would be 'Secure against exploits", but that's outside the scope of my advice).
It's not impossible to be both types of secure, but it is difficult. The main reason both is hard is because to achieve #2, you have to unlock the bootloader which leaves you open to #1 since re-locking it after installing a good custom ROM will prevent the device from working (or brick it at worst).
Achieving #2 is sufficient for me since I don't keep a lot of sensitive data on it, and that sounds like what you're asking.
On my phones that support it, I do unlock bootloader, install LineageOS without GApps, and make sure I have root available. I run few apps, but the ones I do all come from FDroid (or Aurora Store in a pinch).
On phones where I can't unlock the bootloader, my options are much more limited. Typically I'll disable all the Google and carrier services (including Play Services) and disable and replace all the stock apps with ones from F-Droid.