which source would be best nutritionally to consume on a weekly basis?
ghee is 50% saturated while coconut oil is 90%. butter is less fat and more refined. coconut oil also has anti-inflammatory properties. butter has casein and lactose so might be more difficult to digest.
As long as your intake of saturated fats is not higher than 10% of your daily caloric intake, any can go. Depends how you want to use it.
Butter is best for just eating it cold or quick sautéing. No long frying.
Ghee has high smoking point so even frying is fine.
Coconut oil is again good for sautéing, refined one is suitable for frying as well. Just careful with saturated fat.
But it’s best to keep your sources diverse. Even good quality seed or vegetable oil is perfectly fine to consume.