What are the basic daily essentials of a great skin care routine? Isn't it just 1)gentle cleanser, 2) sunscreen, 3) night cream (can be AHA or retinoid)?

Can someone please tell me if what I'm doing is fine? I am DSPW.

Cleanser: Reversa 3-in-1 Mild Gel Cleanser
Facial Water: La Roche Posay sprayed prior to sunscreen
Sunscreen: Dove Deep Moisture Lotion SPF15
Night Cream: alternating every few days - Differin/Reversa glycolic acid 4%

Apparently, the Dove SPF15 is really good at creating and maintaining a healthy skin barrier. It has cell communicating ceramides and linolenic acid, but there are no antioxidants. Is it really such a big deal in my case when I have reacted to any sunscreens that have antioxidants in them? I'm thinking that my Differin is an antioxidant. Aren't fatty acids antioxidant?