Which physical form a shintai takes, a mirror, a sword, a jewel, a stone or a natural feature, is generally tied to the shrine's founding legend or the specific kami enshrined there, a mirror commonly associated with sun linked kami echoing the mirror among the imperial regalia, a sword with storm or warrior kami, and a stone or natural feature with a kami whose identity is bound to that particular place.
How one is established
A shrine's founding priests select and install the shintai at the time of establishment, and in some cases the object is not newly made at all but transferred from a related or parent shrine through a rite called bunrei, dividing the spirit, which extends an existing lineage of worship to a new location rather than starting one from nothing.
Permanence as the whole point
Unlike the paper and wooden objects elsewhere in Shinto practice, renewed yearly and burned without ceremony afterward, a shintai is typically never replaced once installed, wrapped in layers of cloth and boxes that may go unopened for generations, in some cases literally never opened within recorded shrine history, even by most of the shrine's own priests, a continuity of concealment that is itself the object's defining feature rather than an incidental detail.