I’ll recommend a few from different genres:

• Fire Emblem: The Blazing Blade (later FE games also allowed the player to choose between male and female)
• Castlevania: Order of Ecclesia (or Bloodstained: RotN for a newer, but aging, game)
• A Hat In Time (not sure if this is really that old but it’s an amazing platformed)
• any Touhou game
• Life Is Strange (again, not sure if you’d consider this old)