One page a day, torn off by hand.
DayRite is a tear-off calendar for iPhone. Each morning there is one sheet with one verse on it. Draw a finger across it and the page tears away; tomorrow's is underneath.
Torn pages go into History, so any day can be read again. A verse worth keeping goes on the ribbon. A single daily reminder, at a time you choose, is the only thing that ever interrupts.
There is no account and no tracking. The verses ship inside the app, so a page reads without a network connection.