FranticFish - 4:51 pm on Jul 6, 2011 (gmt 0)
Never had that much cash to spend, but if I did here's what I'd try.
Spend cú3K on some cool expensive stuff to give away that relates to what you do (three prizes: 1st, 2nd, 3rd) and then spend the rest on publicising the competition plus FB ads.
See if you can leverage the competition to include submission / voting so that you can attract links (or brand mentions) in some way from that. Can you interview your winners and blog about that or get them to do that?
Or if you're doing it for 6 months why not try and work it into some sort of serial competition with a HUGE load of stuff to be won at the end, again leveraged for content/voting/coverage. Spend 60-65% on the prizes and the rest on seed PR to get the message out there.
Say you do travel, then offer a load of free flights / weekend breaks with the condition that your winners keep a Tumblr or similar autoplugged into FB with your brand plastered everywhere. Make it a quiz where people submit answers and then share with their friends via email, Twitter etc.
People love free stuff; I'm sure any business could find a way to leverage a competition for loads of traffic and links. Might be easier if you're B2B rather than B2C, but with that much money to spend I'm sure you could find an angle.