With source ports, Quake and Quake 2 look better than Quake 3 (in my opinion). But, for multi-player, you'll like 3 most.
Quake 1 - atmospheric, dark, fast, challenging, single player.
Quake 2 - more story, slower, single player
Quake 3 - fast, multiplayer arena shooter (no traditional single player experience. You can play by yourself with bots though).
Quake, Quake 2 and Quake 3 have nothing in common. They should have been called something else completely.
Unreal Tournament 2004 might be more what you want though. That's an arena shooter too (like Quake 3), but that has much better graphics and ragdoll physics.
I recommend you watch a few youtube videos of each to see which appeals to you most.
Thanks. I ended up just getting the trio. I do have all the Unreal Series games that GOG offers.