Which is more effective for whitening ingredients: applying them to cosmetics or taking them orally?

I want to try using glutathione for skincare since it's such a hot ingredient for whitening. However, my dilemma is only deepening as I wonder whether I should buy a topical product or take it as an oral supplement. As I get older, my skin tone is becoming duller and I feel like age spots are appearing, so it has been stressful every time I look in the mirror. I've heard that glutathione is really good for improving complexion.

I'm worried that I might buy expensive cosmetics for no reason, only for my skin to become shiny on the surface without any effect. On the other hand, I looked into supplements or oral film forms, but I heard that the ingredients break down as they pass through the gastrointestinal tract, so very little actually reaches the skin. Hmm... I'm not sure what to do.