You certainly can! But the rules you set can't be made enforceable programatically - that is, the site won't prevent duplicate picks, nor will it give you administrative powers to control behavior that breaks your rules. That said, there are plenty of clubs that create rules, though generally they are rules that are determined by a discussion of a vocal minority of the fans in that club. Some examples:
link,
link,
link.
Each of those clubs have rules that the users have determined that govern how submissions (or a certain kind of submission) should be made. They try to abide by their own rules, but any user is free to break them within the bounds of the Fanpop terms of service. Still, having the rules laid out in advance for users to read is a great idea, and it does help in those clubs.
I think keeping a list of picks and videos is a wonderful idea. I would do it for the
link club (where repeat and spam videos are commonplace), but that the lists I already maintain take so much of my time. Honestly, I'd be crazy to start another. But it's exciting to see someone else doing one, too. More power to you, and bravo for doing something to help others avoid repeats!