I believe that the seller should be contacted directly in the public domain, ie on the topic/thread itself and then arrangement's made in private (hence "dibs" and "PM"). This keeps it simple and clear for prospective 'buyers.' I also feel that if the asking price has been met, then it is the sellers duty to sell the item to them, even if somebody offers an increased sum moments after. My understanding of the 'For Sale' section is that it is an advert, not an auction room, hence why a set price is requested by admin.
Regardless of this, it is down to the seller to establish who he or she would rather sell to, but personally I would follow the moral code. So in the scenario above, I would sell to vulture one.