Personal custom ROM recommendations & reasons why some ROMs had to be avoided.
Let's start with getting the obvious thing off the way - knowing what your device is, what ROMs are available, whether its bootloader can be unlocked & how it's done, how to install custom recovery, & how to install the ROM.
You can start with searching [your device name] XDA on the internet & opening the corresponding forum for the device.
These are what we should expect from custom ROMs in general.
When it comes to privacy, here's a list of what most custom ROMs do :
However, most custom ROMs do not remove / change other Google connections such as captive portal, NTP, & IPv4/IPv6 availability check, let alone document them where it can be easily seen.
Pixel ROMs are consistent in the regard of removing any non-Google preinstalled corpo apps, & that's about it. As for Limbos, they're too inconsistent in this regard, either flip-flopping from Vanilla to Vanilla/GApps / GApps-only, and/or supporting some devices as GApps-only while leaving others to Vanilla-only / Vanilla/GApps, depending on the maintainer's whims.
Examples of some outliers :
Most ROMs will run a Quickstep-based launcher (which looks & feels like the Pixel launcher), except for /e/, which uses BlissLauncher, an iPhone-like launcher. The stock launcher can be replaced with third-party launchers like Nova, OpenLauncher, or Neo Launcher though.
For the settings menu, most ROMs will take this approach : Take AOSP settings, add a custom-named advanced settings, and / or add some additions in the default settings. Occassionally, some custom ROM (mostly Limbos) will also change up the settings UI, which can make them either look better or worse.
The difference you'd see will be the amount of customizations, the boot-animation (which can be changed by changing the bootanimation.zip from /system/media), & the prebuilt apps (sometimes the UI as well). Aside from all of them, what you'll get is AOSP, with some mods here & there, sometimes crammed onto an aptly-named "advanced settings". And, if we take GrapheneOS and /e/ into the equation, the captive portal & network time server. GrapheneOS, DivestOS, & CalyxOS are the only ones to document the default connections where it can be easily seen.
Here are the ROMs you should avoid.
Always avoid these kinds of ROMs. They're basically similar to the stock OS found on Pixel PDAs, but with arguably more features.
Here's a short list explaining why you must avoid all Pixel ROMs :
Generally, you should avoid them. While they do provide Vanilla variants, odds are that they'll support your device as GApps-only. An exception to this norm seems to be crDroid as they mostly release Vanilla-only, with the sole exception of the GApps-only OnePlus 7T "Pro".
Here are the examples of Limbo ROMs you should avoid :
Go-ogle spyware, spywares from the stock ROM, custom vendor firmware that probably don't work with custom ROMs, & custom kernels not working (or have some issues), perhaps by design. Don't bother unless being a slave is more important to you.
At the moment, there's no ROM I can recommend without regret as they're either missing essential features and/or have user-hostile sites. However, regardless of whichever custom ROM you're running, you're mostly going to be dealing with the apps you've installed once you get the ROM tuned to your specifications. As for which ROMs I will personally recommend, I've moved the recommendations to a separate article.
TL;DR : not using a phone > Any proven custom ROM of choice (my recommendations list includes some of them) > Vanilla Limbo > Pixel / GApps-Limbo / GApps version ROMs > Stock ROM.