Not sure why, maybe caused cause I mostly work with spot lights.
Spotlight are good. I could be wrong, but from the shadows it seems you're using point geometry for your lights like
Saki_Sliz said. It's sadly the default setting and a lot of people get confused by it. Be sure you have your light panel somewhere to modify your spolight setting. Everything you need is in the light section.
Most important setting is light geometry and it's size. Most used geometry are Rectangle or Disc (Sphere sometime but you could use pointlight for this). Point geometry is mostly never used outside very few case like "flash" camera effect. Height & width define the size of the Rectangle or Disc, don't hesitate to try different numbers (25*25, 50*50, 100*100, 300*300 and so on). The more larger, the more soft are the shadows (distance play a role too). Spread angle defines the size of the angle that the light will cover, so basically from 0° to 180° (default is 60° but lot of time you need more). Turn render emitter OFF so geometry of the light will be invisible (but will still show on reflexion like glass and eyes). And of course increase the lumens until you're satisfied.
Rule of thumb for a good lightening, imo, is to keep it simple. Don't add source of light (especialy if they "cross" each other) if you have not a good reason for doing so.
