In no particular order and limiting it to 10:
Prince of Tennis OP 7 - Dream Believer: https://www.youtube.com/watch?v=7Uu7caB0OWI
The Unlimited Hyobu Kyosuke ED 2 - Brightest Light: https://www.youtube.com/watch?v=kHyRZY3Hb8s
Sousei no Onmyouji OP 2 - Re:Call: https://www.youtube.com/watch?v=blD1-ekFg9U
Samurai Flamenco OP 2 - Ai Ai Ai ni Utarete Bye Bye Bye: https://www.youtube.com/watch?v=Gdp4eGiU6Oc
Oshi no Ko ED 1 - Mephisto: https://www.youtube.com/watch?v=A48bcNyi1VM
Bakemonogatari OP 3 - Ambivalent World: https://www.youtube.com/watch?v=P0meri63JJ4
Bakuman ED 2 - Genjitsu to Iu na no Kaibutsu to Tatakau Mono Tachi: https://www.youtube.com/watch?v=C4BzBNmozKI
One Piece OP 2 - Believe: https://www.youtube.com/watch?v=54dp8ucsGG8
Bleach ED 17 - Hitohira no Hanabira: https://www.youtube.com/watch?v=MFTxGRE0BZI
Slayers Try ED 1 - Don't be Discouraged: https://www.youtube.com/watch?v=ByiqLpt6kKg
Okay, here is a good variety ones you can look into (since you say you have played Minecraft together, I'm assuming that these recommendations don't necessarily need to be couch co-op, and by 'not graphic intensive' you mostly mean a game that can run on a computer that can run Minecraft on low settings)
BattleBlock Theater (platformer)
Keep Talking and Nobody Explodes (bomb defusing)
Hammerwatch (series of hack'n'slash games)
Don't Starve Together (survival)
Risk of Rain 2 (rogue-lite)
I have also seen Overcooked, Terraria, Portal 2, and Stardew Valley have already been recommended. Those are solid ones as well
Monster Hunter may be too much for your computers, but if you would be interested in a similar game that is lighter weight, you could look into God Eater (1 & 2 are bundled together)
Also, if you end up having any interest in branching out into vs games, you could look into Crawl, SpeedRunners, Screencheat, Ulimate Chicken Horse, and Lethal League
You mentioned you know you missed a bunch and I can fill in a couple of holes, since you missed 4 of my favorites this season (all of them are not as good as Dandadan or Shangri-la Frontier, but better than Demon Lord 2099 imo).
Going from best to worst:
Tower of God S2 cour 2: It definitely isn't as gripping as S1 still, but it's setting up some pretty interesting and exciting developments. It's a difficult show to explain or sell without spoiling a lot of stuff, but I definitely do recommend it.
Mecha Ude: A solid sci-fi show where people can combine with sentient mechanical arms to battle. It gives me similar vibes to a more family friendly Kill la Kill or the DragonBack book series. Hiroyuki Sawano was involved with the OST, and the animation and characters are decent. My only gripe is that some of the plot points felt a little contrived, but it doesn't feel like the kind of show where you should be terribly concerned with that to me.
Acro Trip: A comedic spin on the magical girl genre, a middle school girl gets tricked into joining her local evil mastermind to battle against the local magical girl who she admires. It's one of the most family friendly shows I have ever watched and still snuck in some hilarious/ridiculous jokes that would go right over most kid's heads.
Blue Box: pretty standard anime romcom, but also has some solid anime sports going on at the same time. Overall, it's just two genres that you wouldn't normally expect going together being blended together very well.
As far as some others that I didn't enjoy quite as much goes:
Kinonoinu: Author who is depressed because his childhood dog died finds a mushroom dog. It's not bad, it's just really slow, which I'm usually not in the mood for.
Hitoribocchi no isekai: Self proclaimed loner gets isekai'd with his entire class and nobody will let him be alone. Standard garbage isekai.
Goodby dragon life, hello human life: Dragon gets reincarnated as a human. He meets a lamia and a descendant of the hero who killed him. There is a weird running "joke" in the show of how much everyone loves the milk from the cow girl. Honestly, nothing else interesting enough to be worth mentioning happens.
Negaposi angler: A college student who is depressed because of debt and failing health picks up fishing. It's not bad, it's just really slow. I'm not much of a fisher myself, but from reading the comments on the episodes, some of the fishing tips sound pretty legit.