I recommend Unreal Tournament 2k4, specifically the Assault maps with the AI. They give you a rundown of how you need to attack and progress within the time limit, then you get the chance to be the defenders and stop the AI from beating your time. It’s just a fun old FPS with cool futuristic guns.
Another is Killing Floor 2, it’s a survival FPS fighting “not Zombies” called Zeds. Pick a class, kill enemies, earn money, buy better guns, level up, survive a set amount of waves, kill the boss, then pick a new map and do it again. You can unlock cosmetics and as you level up you can try harder difficulties. I got it on my PS4 and have been enjoying it for over 6 years.
PlayStation has the better exclusives, but a lot of kids have Xbox so they might want that if their friends play online.
I have personal reasons to not get Xbox (lost faith in the brand years ago) so I will hype up PlayStation to no end and talk shit about Xbox until the heat death of the universe, but if it’s for your kids then get them what their friends have so they can play together.