Hi,
I have already built and I am hosting a FB app for sweepstakes, it also features a number of other different types of competition's, such as instant win.
The app features one entry per user, fan-gating (users must like you before entering), plus (optionally) 'viral' referral features - users get extra entries if they get their friends to enter. Once the competition is over, the app can also pick a winner and notify them, and show you stats on the number of views, entries etc.
The App is fully hosted and includes the entry form design.
Regards
Alistair Knight