To make the case that Edmund is the most interesting of the three villains, one could talk about Edmund’s relationship with his father. His dad doesn’t treat him nicely. As with the rest of society, Edmund's dad marginalizes him by referring to him as a “bastard.” One could argue that Edmund’s machinations are the most interesting because his bad behavior makes the most sense. Edmund is getting back at the world that has maligned him. The case for Edmund being the most interesting villain becomes stronger since, by the end of the play, Edmund drops his double-dealing and tries to save King Lear and Cordelia.
As for Goneril, one might say that she’s the most interesting villain because of how ungrateful she is to her dad. Her dad just gave her a large chunk of his kingdom and she repays him by kicking him out of her house. Yet, as with Edmund, Goneril’s actions have some justification. It is rather rude to bring a big group of “riotous” knights to someone’s home. Alternately, Goneril might be perceived as the most interesting villain because almost all of her other steps are about an acute desire for power and dominance. She has no reason to poison Regan other than to knock out a potential competitor for Edmund.
To state that Regan is the most interesting villain, consider how her conduct compares to Goneril's. Like Goneril, Regan doesn’t want her dad to stay with her. However, Regan summons Goneril so that they gang up on their dad together. More so, while Goneril suggests plucking out Gloucester’s eyes, Regan wants to “hang him instantly.” Typically, Goneril is portrayed as the evilest sister, but it might be interesting to use the previous examples, among others, to claim that Regan is as malicious.