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👍)
https://www.youtube.com/watch?v=4VfU4A0Qs6M Escaflown
https://www.youtube.com/watch?v=euX_8PYBvr4 Attack on Titan
https://www.youtube.com/watch?v=RR6kzUMimSI Ikouze Paradise
https://www.youtube.com/watch?v=uO0LjrlyNwE fractale opening
https://www.youtube.com/watch?v=Auqu-_VHLMw X 1999 opening
Origa from GIS also nice but was already posted. The touhou games also have some really cool music. Even tho I dont play them.