Sega Saturn
Yeah, Saturn.
It is the most underrated classic console: Huge quantity of arcade style games, good 2D/3D fighting games, shoot 'em up games... Fast fun everytime you need. Also, some good RPG games, if you want.to lose time.
But among N64 and PSX? N64, no doubt: Wave Race 64, Star Fox 64, F-Zero X, ISS64, Super Smash Bros, F1-World Grand Prix, ... they are GREAT and have a very "arcade" feeling (you can play them 5-15 minuts with total satisfaction) and they were top in its time. Also the WWF games, or Mario Kart 64 (though, this last is one of the games I believe aged worst from N64, but it can be very fun nonetheless).
Even Super Mario 64 has a very arcade gameplay: you have to open doors and get 2 keys to have all the world open... but its feels very OPEN world, and in no time you can open lots of its worlds, and it plays and controls fantastic, from second 1, even today (the SM64 is the king of the speedrun games: they are AMAZING... even beautiful to watch).
Also, Sin and Punishment, never published in western countries by then. And of course Goldeneye/Pefect Dark multiplayer. As multiplayer games, you also have the turoks, mario parties... the mario tennis and mario golf.... man, i don't know, it is a great machine.
And a memorable mention to Pilotwings 64, an early underrated gem: flying and exploring in that game, especially in the mini US map, just for the pleasure of doing it, can be very therapeutic or cathartic. Is like a pre GTAV, just going around the world with a car/bike, but in the air.
Nintendo 64 is superior in "instant fun" classics. And NO loading times at all. And nobody cares a fuck about the old CGIs of the CD games since 25 years ago, so N64 wins again: Those CGIs maybe sold games then, but they are very ugly, stupid, and sometimes you cannot even bypass them.
PSX is for LOOOOOONG and time consuming games: Lots of Japanese RPGs.... or a long 1 sit gameplay in one survival horror with tank controls.
Also, you can play some classic 1vs 1 fighting games (DoA, Soul Blade, Tekken series...). But in this last case, I prefer to play Fighters Megamix for the Saturn. Much more fun and with many crazy unlockable characters. It also have that smash bros feeling, years before the first smash was developed, but in a classic 1 to 1 fighting game.
Oh, and many famous racing games in PSX, but many of them are not that good now (and N64 also have some good racing games). And no... no Gran Turismo 1 and 2, please (those games need all your life for themselves to start to get really interesting content, and they do not have any deformation and damage physics, like others did already).