The entry function is probably the most familiar to people but different manufacturers use entry to describe locks with subtly different functionality. ANSI F13 is the least complicated to use because it doesn’t have a toggle switch to lock the lever on the outside of the door. There is only two ways to lock the door, with a key from the outside or with a thumbturn from the inside. You can’t lock yourself out unless you lose the key somehow or the lock malfunctions.
Other entry functions have toggle switches that will mess with you and may behave in unexpected ways for dog walkers or house sitters who are incidentally some of my most frequent customers for unlocking doors. Oftentimes they are flummoxed by locks with ANSI function F11. It remains locked from the outside even after retracting the deadbolt! This is very confusing for those with no experience with mortise locks.
An entry function L series cassette from Schlage are $233.