There is an out-of-universe explanation for the appearances of the Sith, which George Lucas made fairly clear in interviews in the run-up to the release of the The Phantom Menace. Each of the Sith who appear in the film was designed to strike a chord with a classic image of terror.
The first Sith to appear was Darth Vader, whose outward appearance was very much that of a robotic entity—faceless and seemingly inhuman. The inherent evil of is robotic nature is mentioned specifically in the movies; Obi-Wan thinks he is "more machine now than man, twisted and evil."
The Emperor, from his first appearance as a face in The Empire Strikes Back, then in person in Return of the Jedi, was an almost prototypical evil wizard type. His visage was twisted in a way that suggested extreme age, but also that some other preternatural effect had probably contributed to his disfigurement. The Emperor also uses a somewhat different suite of Force powers than the Jedi knight characters (Luke, Obi-Wan, and Vader) in Return of the Jedi. He does not fight with a lightsaber, but rather the more wizardly Force lightning. (Ian McDiarmid said that he was very surprised that he was going to be fighting with a lightsaber in The Phantom Menace, as it did not match his conception of Palpatine's character.)
Although Darth Maul's design went through a number of iterations, and the design elements that eventually became his horns were originally intended to be more like feathers, George Lucas decided to make the character horned because horns were a common feature of many scary monsters, in multiple religious and folklore traditions. (This is discussed in the Bill Moyers interview linked to above, which may be the last interview George Lucas gave in which his original thoughtfulness about Star Wars comes through, without the need to disingenuously defend the decisions he made for the prequel trilogy.) So Darth Maul's visage is essentially that of a classic demonic foe.
Christopher Lee as Darth Tyranus embodies a different kind of classical image of evil—not the monster, but the betrayer. He is handsome, silver-tongued, and beguiling.* He is a dark knight, a character type that is referred to obliquely in several additional ways: the fact that he holds a noble title (count); his status as explicitly being a former (i.e. fallen) Jedi; and the fencing-sword styling of his lightsaber.
Personally, I think that the nature of the Force (at least as portrayed in Lucas's films—and especially the original trilogy, if the original releases are considered to be a full alternative continuity) is that the evil Sith who use the powers of the Dark Side will naturally be transformed into a shape that embodies their evil, whether that makes them horrifying, uncanny, or whatever. However, there does not seem to be any hard rule about by what means this should happen; the disfigurement of the Sith lords seems to be destiny, but not very predictable.
*When I saw Lee as Count Dooku in Attack of the Clones as the newest Sith, I was reminded of an old Dragon magazine article outlining an anti-paladin class. It said that the charisma score for an anti-paladin was to be determined by a special procedure:
[T]rue Evil will either reveal itself in all its hideous ugliness or disguise itself behind a pleasant exterior. For this reason, Anti-Paladins tend to be either sinfully ugly (4 or less Charisma) or devilishly handsome (17+).
Vader, Sidious, and Maul were all in the "hideous" category, while Darth Tyranus was "devilishly handsome."