Our school building is _____ dilapidated.

The blank requires an adverb that modifies 'dilapidated' (in a state of disrepair). 'Visibly' means in a way that can be seen, which appropriately describes how the dilapidation is apparent. 'Little' is not typically used to modify 'dilapidated' in this way. 'Deeply' refers more to emotions or thought. 'Satisfactorily' suggests a positive quality, inappropriate for 'dilapidated'. Hence, 'visibly' is the correct choice.