Weapon Supremacy is like level 18 or 20... I wouldn't build for that if the game's starting at 1. It is extremely rare to see a game actually last that long, and when it does, it probably takes 1-3 years to get there.
If Swift Hunter is allowed, obviously he should be a Scout/Ranger, though with the book selection he's going to have a tough time moving 10+ ft and full attacking, and Greater Manyshot, much as I personally consider it a trap, isn't even available, either.
If it's not, I'd do the rogue archer, or if he doesn't want that... a Ranger X / Fighter 4 build w/ Ranged Weapon Mastery, I guess. He won't have access to any of the ranger spells that actually make rangers good archers (like Arrowmind, Hunter's Mercy, Hawkeye, Arrow Storm, etc... the core ranger spell list is by far and away the worst one in the game), sadly. But not sure what other full BAB class in those books would actually benefit archery more. Is UA allowed? Maybe Barbarian with Whirling Frenzy if so? The bonus attack is not restricted to melee only. You'd either need two different bows or beg the DM for a str-adjusting bow, though.