I just use the old lock set that was on the door, but I leave it locked all of the time. My wife and I like how this works because combining this with my strike set to fail safe, the door continue to work "normally" for my non-technical family and friends.
However, we have also closely considered a "classroom lock". For these types of knobs the exterior portion stays locked at all times, and the interior side remains unlocked at all times. There is no locking switch.
A few items for you to consider:
Have you considered the loading issue with electronic strikes? There are several discussions on this board that touch on it. In short, almost all strikes on the market are unable to unlock if they are loaded. The slight pressure your door seals create is enough to prevent an unlock. This is why you always see big air gaps on commercial doors with electronic strikes.
I am only aware of one door strike manufacturer that makes a "loadable" strike. They are HES. There may be more if you search.
Two, read up on how door latches work. There are typically two pins. When installed properly and the door is closed, only the larger pin should be extended. The strike should keep the smaller pin depressed. This mechanism is used to prevent a credit card from opening the latch. If only the large latch is extended, then you will not be able to push it back into the door. If both the large latch and the smaller pin are extended you will be able to simply push them back into the door.