I'm going to stick to my ultimate favs here.
Mamamoo was a lot harder for me, due to sheer song count, but....
Mamamoo:
Reasons:
Seems like the best combination of all the things Mamamoo became famous for--ridiculous vocals, versatile concept, incredible energy, sexy but mature vibes. It's not even a top 5 Mamamoo song for me, but it's a great representative for them. You will not come away from an Egotistic performance not knowing what Mamamoo is all about.
If not Egotistic, I'd choose Um Oh Ah Yeah.
NewJeans was easy.
Reasons:
I have introduced many to NewJeans through the best K-Pop song of the decade. The y2k aesthetics, the addictive choreography, the chorus, the soft vocals, absent any screechy high notes or mandatory raps--this song will always be THE NewJeans song for me. The essence of the group and even individual members are layered all throughout this song and its many MVs.