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
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