Depending on the type of finches you keep you'll need an entry hole of approximately 4-5cm (1.5-2inches). This tends to be the average size of the commercially sold finch breeding boxes.

Hope this helps

 Yes, you don't want to make the hole too big. It would result in larger birds or even squirrels venturing into the bird house.

 I will say, based on my own experience as a watcher and house provider that finches like a small opening no larger than about 2" around.