Daryl,
From what you've described the first place I'd look would be the groove for the string in the nut. If all other strings don't buzz when played open it sounds like the 6th string has cut itself too deep in the nut, and that's why it buzzs on fret 1. When you barre a chord (say an F position) you're taking the nut out of play, so depth of groove doesn't matter, and 6th string sounds fine.
Solution - de-string, remove nut (should only be glued in position), fit new one, should be fine. Before removing nut check the groove depth, so you don't waste you're time and money. If that isn't the fault I think you need to consider possibility the neck is warped, but I'd have thought this would have a greater effect than just 1 string. Best of luck!
VinylPete
February 2009