Here is the list of characters and respective missions in which they are unlocked:
Story missions:
Franklin Clinton - Franklin and Lamar
Michael De Santa - Complications
Trevor Philips - Mr. Philips
Amanda De Santa - Marriage Counseling
Brad Snider - Prologue
Tao Cheng - Trevor Philips Industries
Dave Norton - Dead Man Walking
Devin Weston - By The Book
Fabien LaRouche - Fame or Shame
Floyd Hebert - Friends Reunited
Jimmy De Santa - Father/Son
Lamar Davis - The Long Stretch
Lazlow Jones - Fame or Shame
Ron Jakowski - Nervous Ron
Patricia Madrazo - Caida Libre
Simeon Yetarian - Repossession
Solomon Richards - Mr. Richards
Steve Haines - Three's Company
Stretch - The Long Stretch
Tanisha Jackson - Lamar Down
Tracey De Santa - Daddy's Little Girl
Wade Hebert - Mr. Philips
Strangers and Freaks:
Beverly Felton - Paparazzo
Cris Formage - Unknowing the Truth
Dr Friedlander - Chaos (Accessed by visiting Friedlander as Michael after the mission Marriage Counseling)
Maude Eccles - Bail Bond
Mrs. Thornhill - Mr and Mrs Thornhill
Credits: GTA Wiki
https://gta.fandom.com/wiki/Director_Mode/Actors