Best Serious Sam for Multiplayer

Multiplayer what? PvP or Co-op? SS3 should be the most oriented for PvP but Fusion should now soak up quite some of it, while TFE HD and TSE HD should be the better for co-op.
And Serious Sam 2 does not exist or ever existed.

played SS3 for local splitscreen / couch co-op. really loved that i could actually choose to whether to split 2-player screen horizontally or vertically (cuz horizontal splits are the only right choice but at least vertical isn't forced on me like in sphincter cell or rainbow sux)... IIRC there were also options for how to split the 3rd player. Gameplay itself was ok... wasn't Gears of War, but since you're asking about the SS series specifically, I assume you know that much.

CoOp-wise I'd say the Encounter ones over BFE and actually none for PvP though, there are better games out there for that tbh. Maybe worth some consideration is also the newly released Bogus Detour.