I suspect your generous donor would like some mileage out of his contribution. The contest approach has appeal in that direction. A random draw from whoever hears about this and mails a card in might not be as good. A drawing among existing members (however qualified by # posts, duration or whatever) is probably the worst.
All that said, I probably wouldn't enter a contest. I don't need the scope that badly, and the effort to reward ratio just isn't there unless there is almost no effort. It seems likely that there will be several thousand entries (7000 members of this forum, an unknown number of uTubers, and whoever else finds out about the contest), so the chances of winning will be quite small.