Lighting from the side - evokes stronger character, more dramatic, frames half of face in harsh light, but keeps other in 'mystery' (shade basically).
Lighting from above/below - consider this as well, but for different character types.
Harsh/Soft Lighting - for relatable, relaxed atmosphere, go soft, for more formal, gripping character/atmosphere, go harsher. Also consider warm and cold tones.
Colour palette - when one side is lit in (blue, yellow, etc), shade in the opposite complimentary colour for a better effect (orange, violet, etc). In summary, use this technique for a more engaging image/scene.
Framing - depending on the set, close ups and long shots are equally as dramatic and engaging, but in different ways. (e.g. Queen's Gambit cover, Split cover).
Set - a variety of backgrounds, props, and lighting strung together have different effects, but keep in mind not to keep it too crowded or too bland. Don't rely solely on one element to give a full effect.