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Since you have an unlocked bootloader, it's generally as simple as downloading the latest LineageOS and the lastest TWRP, flashing TWRP with fastboot, then using TWRP to wipe the system and sideload LineageOS with ADB. The whole process is explained here:
https://wiki.lineageos.org/devices/mako/install
Installing Google services and Play Store are extra steps that are covered in the LineageOS documentation.
If you want to run without Google services but do want mainstream apps to work, you might consider installing the LineageOS builds from MicroG instead of the official ones: https://lineage.microg.org/
MicroG spoofs the existence and some of the function of Google services to apps that require them. But not every app works smoothly with MicroG, so it depends on your willingness to live with bugs vs. deal with more tracking using Google Services.
If you do install the MicroG version, it will have the Fdroid store built in. From Fdroid, you can install Yalp Store or Aurora store to download apps anonymously from Google Play Store, or they call allow you to sign in to download your paid apps.
If you only want to use open source software and do not need or want Google services or any imitation of it, then you can simply install the official LineageOS version, download Fdroid, and get your open source software from there without ever using MicroG or flashing Google Apps.