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👍)
I'd add a couple more to your list.
Highschool of the Dead opening - https://www.youtube.com/watch?v=M8tRBup0j9E
Attack on Titan opening 1 - https://www.youtube.com/watch?v=PDHCLjuOzXY
Hunter x Hunter (2011) ending 2 - https://www.youtube.com/watch?v=6FhmyWT-_0U
Tengen Toppa Gurren Lagann ending 1 - https://www.youtube.com/watch?v=5EXFilTUiko
Mirai Nikki opening 1 - https://www.youtube.com/watch?v=DbqykQH1ZME
Noragami opening - https://www.youtube.com/watch?v=gWCnKoEgfP0
And on a completely different theme, here's another one that I like:
Mahou Shoujo Madoka Magica Soundtrack Volume Two opening track - https://www.youtube.com/watch?v=HcgEHrwdSO4
lol wtf did I just watch?
Hey, it's a good song.