One thing I've really gotten to like about anime music is that rock/punk seems to still be pretty popular in Japan, whereas it's been virtually entirely replaced by rap/autotuned club music here in the US. I can't understand a lick of the lyrics, but a ton of anime has really catchy and upbeat punk, and as a 90s teen, it brings back fond memories. I'm a (marginal to average) drummer and a lot of the songs aren't too hard to play and a ton of fun.
I'll start by saying Tu Love Ru's season one opener "Forever we can make it" by THYME (also the animation that goes with it in the show is👍)
Okay, so... I saw someone say Yoko Kanno, who is a firm favourite of mine, but noone's brought up my favourites of her works. Presenting concert versions because I can:
Macross Frontier Op2 - Lion
Macross Frontier Ed2 - Northern Cross
Macross Frontier Ed1 - Diamond Crevasse
Also - Diamond Crevasse from 'Macross F Galaxy Tour FINAL in Budokan' - I'm including this version primarily because it ALSO has Yoko on the piano. Honestly it's a strong candidate for my favourite song of all time, even if it reduces me to tears every time I listen to it.
Other ones I've not seen mentioned:
GATE op2 - Sekai o Koete
Azur Lane (anime) op - Graphite/Diamond (yes, I like May'n, can you tell?)
Gundam 00 Op2 - Ash Like Snow
Bleach Ed3 Houki boshi
Dude GATE was fucking sick