If anyone has Bill and Ted's Excellent Adventure,  then they'd know that the phone booth doesnt slowly fade into existence like the TARDIS does, It drops out of a glowing hole in the sky,  or into a glowing hole in the floor.  Although it was blue in the movie,  i'd think it would look better in white as it is shown in the second animation.   The portal it drops through would adjust its size for your exterior of choice, since some like the Vanilla and floral exteriors are bigger than the rest. No noise plays as it drops out of the portal in the original movie,  so perhaps the noise made by the vortex manipulator would suffice?  when the box hits the ground it would play the flight pannel noise of the tardis hitting the ground. Below  i have some clips to show the animations.

Clip from the actual movie

Fan-made animation test

This animation is kind of similar to the Ender dragon's death animation,  yet without the explosion or fancy lightshow.  When the TARDIS begins to demat,  its texture will slowly disappear pixel by pixel.  When Rematting, the same animation will play in reverse, where the TARDIS slowly builds itself together.

highly detailed exteriors like Ed's exterior would need large chunks taken out of it one at a time due to its textures high pixel count. This would have the regular Tardis Demat/remat noise

This Animation is Similar to Deconstruct animation 1,  but different enough i felt it needed its own section.    The Tardis exteriors, are made of shapes,  this animation would take it apart, shape by shape until nothing is left,  and the same animation in reverse when you remat. This would have the regular TARDIS remat/demat noise.

This animation is one of my favorites, because of how simple it is.    This animation consists of lightning striking the place of landing (not actual lightning) and an explosion particle along with the lightning and explosion sound effects instead of the tardis noise. When the dust settles, the exterior is standing there proudly.     When Rematting,  The same animation will be played, but the Exterior will no longer be present after the particles end.

The Growing animation Would work best with organic tardis exteriors, the floral exterior (still would like some in other tree variants pls).   Dematerialization would consist of the Exterior slowly withering and shrinking as a plant dies,  and then dissapearing. Rematting would put a super tiny version of the exterior on the ground in the place of landing, then have it grow to its full size. This could be silent, or SFX could be found later.

This is an animation suggested by Dhi_awesome.  This animation would consist of explosion particles (and noises)   and once they clear the Exterior stands proudly, as in the zeus animation.  The same goes for the demateralization,  except once the explosion particles clear, the exterior is gone 

This animation was suggested by TheGingerDoctor.  The Demat animation would consist of flame particles coming out of the ground and enveloping the exterior hiding it completely from view, with the minecraft  Fire SFX instead of the regular tardis demat/remat noise

This animation is similar to nether sent, but with end particles and sounds. The enderman's 'stare' sfx that you get when you look it in the eyes will play as ender partiles slowly envelop the exterior. Then the sfx an enderman makes when it teleports away will play, and the exterior will be gone.   When rematting, the same animation will play,  but at the end,  it will play the sfx an enderman makes when it teleports TO you.

This animation was also suggested by The ginger doctor.   It would consist of the TARDIS slowly turning white till its glowing.  While the engine noise plays super slowly in the background,  then it would slowly fade out of existence as the engine gets more and more faint.  Rematting would consist of the pure white glowing TARDIS fading in, then slowly going back to its normal colors.

This animation was suggested by G0ld3n_Phant0m.   It would consist of the TARDIS exterior shattering like glass and disappearing.   whether or not this would be done through models or particles up to john if he decides to add this. though particles would probably be easier then getting shard models of every exterior.  The remat would consist of all the shards rising up out of the ground and forming back together to make the TARDIS at the point of landing.