Radhruin beat me to it ...
... pointing-out that Sauron had never been a Balrog. However, this,
must be contested.
Originally Posted by YamydeAragon
On the one hand, when the maiar were manipulating ephemeral, insubstantial forms this statement can stand. On the other hand, physical incarnation required a lot of time and/or effort to achieve: Sauron required a lot of time (and the survival of the One Ring, which contained a substantial portion of his original native power, was also necessary) to re-manifest after the Downfall of Numenor, and he indeed became restricted in that he could no longer assume a beautiful form; cast down by the heroes of the Last Alliance, with his Ring 'stolen' (but, again, not destroyed), he required c. 1000 years to 'compose himself' yet again. The Istari were sent to Middle-Earth in shapes ordained for them by the Valar, and Gandalf was able to reincarnate as 'the White' only because he was 'sent back', 'his task unfinished'; even so, it is apparent in the narrative that Gandalf's transformation left him "discombobulated", and he needed time to collect and order his sensibilities, and recall the memories of his former incarnation.
I do wish to add clarification to the other issue: a Balrog had chosen (likely at Melkor's urging) to seize power in an entirely corporal manner, by investing its energy into an 'awe/fear-inspiring hroa of great strength and power'; Sauron's choice was the more-subtle one, preserving his innate 'maia-perspicacity' of thought and form, becoming 'sorceror', 'necromancer', and 'ring-maker'.