German for "single cylinder entrance handleset"

I've decided that I no longer want to put up with the typical European door locks. I will be shopping for a "normal" (for me) deadbolt lock that can be set to either automatically lock the door on closing (using the latch), or keep it unlocked when shut (latch can be opened with lever on handle). I also want the little turn handle on the inside so that anyone inside can both lock and unlock the door (deadbolt) without using a key, but a second person from outside would still be able to unlock the door using a key.

In English I'd be looking for a single cylinder deadbolt lock with a lever/handle, aka entrance handleset with deadbolt and latch. The set looks something like this one:



What the heck should I be asking for in German when I go to the baumarkt?

Take that picture you posted along with you and show them maybe?

Yes, that would probably be the easiest rather than trying to explain something so foreign. Will try to also find a view of the side to show exactly how the latch and deadbolt should work. Thanks!