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👍)
The 2 opening songs for Ghost in the Shell: Stand Alone Complex. They stand out particularly because they aren't sung in Japanese and occasional Engrish, but rather in Russian with Latin and English peppered in. Furthermore, it is Industrial sounding music (or is it dance club music? idk), which makes it stand out even more among other anime openers. The singer for these songs (RIP) has other material you could check out if you end up liking these.
Opener 1, plus full version
Opener 2, plus full version