I discovered Gorillaz probably a while ago. You know 19-2000, that one song from the low quality compression spinning memes? Someone played it in a chatroom radio I was tuned into and I really liked it. So that song was just sitting on my playlist for a while until I actually bought the album it was from. I strictly listen to new music physically unless there is no way I am getting a CD of it at a physical store.
Phase 1 and Self Titled have to be my favorite stylistically. The songs are so fresh (but visibly a lot less professional than their later records), and the artwork has so much expression and charm! My favorite songs are all the singles, Re-Hash and Sound Check (Gravity). It's good shit. I haven't listened to all of G-Sides yet but it also seems pretty dope, I like Ghost Train.
The Gorillaz G-Bitez also came out of this phase, and are a highlight of the characters for me. These were a series of animated shorts depicting the characters in various situations that were once watchable on the Gorillaz interactive website, and can be found on YouTube. My favorite is The Eel!

PHASE 2

The second phase of Gorillaz also has indubitably my favorite album release. Demon Days is non stop hits with not a single song missing. My favorites are Kids With Guns, Dirty Harry, November Has Come and DARE.
PHASE 3
You could say it took me a while to write about my opinions on Phase 3. Not for any particular reason, outside of me not having experienced much of it. My copy of Plastic Beach on CD has been broken for the longest time (chuckle-inducing to be writing this part listening to Broken), so I've only heard a couple select songs and the singles. Let me take a moment to write about it anyway:

First of all, this album's setup is amazing. Plastic Beach is canonically written solely by Murdoc and 2D, with assist guitar riffs by Cyborg Noodle, who Murdoc built using Noodle's DNA after she got lost filming the music video for El Manana. Unable to draw influences from the missing members, and with 2D being held captive for most of its run, this record is unapologetically Murdoc's. And, somehow, what came out is a profoundly beautiful synthetic sound...?
The tracks Plastic Beach and Broken come to mind. The album's sound I believe to be full of artificial instruments and samples on purpose - it's a commentary on climate change and plastic pollution. As grim as it may sound, it comes out perfectly suiting my taste, emitting a feeling of melancholy, largely helped by the vocal performance.