My "must have" non-core mods summary:
In the game I play for my own personal enjoyment, I use mods to stop coughing while eating/grilling, stop the nose picking animation in toddlers, prevent fish from dying/being eaten, prevent minor pets from running away or dying, prevent death from jellybean bush, remove the stir crazy and saddlesore buffs, prevent fleas, prevent food spoilage on the counter and in the frig, prevent the horse twirling animation while saddling, various game fixes, no burglar, no meteors, no juiced buff romancing autonomously, various other no autonomous mods, ITF large flower unhider plus no autonomous dew throwing, cheaper lifetime rewards, showtime extras unhidden, tweaks to dragons, tweak to leaf raking, keeping the MF pics from changing at night, a softer light/less bloom lighting mod, Cinderelli's recent mods, a decensor, stencil unlocking mods, object mods for fixes and some objects mods that make things recolorable, and etc, etc, etc. Some mods I have recently found, and will be testing before I decide to add them. I am currently in the process of finalizing my mods, and want to be sure I don't miss any I need, for the future.
I use mods from all the websites I talked about, earlier.
I also have a totally and completely unmodded game I use for testing purposes.