SIN Bahamut wasn't in the game, but it's definatly it according to official sources. The Neo and ZERO were two of three incarnations in the game, which is why I think they went with SIN, since it'd be kind of... thoughtless to favor one over another regarding the game, because after all, the player might not have gotten regular, Neo and ZERO, and therefore Cloud wouldn't have it in AC. Remember, you had to pick the summon materias up yourself, and if you didn't, there was never going back. Not to mention ZERO itself is a culmination of having the previous two.
As far as WEAPON goes, well, WEAPON's are the guardians of the Earth. You don't really summon them.