How do I collect daily login statistics
I would say use the User Points module along with the User Points Login add-on module to handle to recording of points for users logging in.

Then you can use the Views module to build reports for yourself to see which users have the most points for a given period.

It would also be possible to use the Rules module to automatically email you a report of the winners at the end of every month and then reset all user points to zero (I'm making an assumption that there is a rules action you could use to remove existing user points).