First step is good cleansing. Try double cleansing - first oil based cleanser balm like Body Shop Camomile Balm Cleanser, Clinique Take the Day Off, Hada Labo Gokujun Cleansing oil or Pixi Double cleanse. 2nd cleanse: Go for a gentle, non foaming cleanser. Good ones are Avène Extremely Gentle Cleanser, La Roche Posay Toleriane Dermo Cleanser or CeraVe hydrating Cleanser.
Sunscreen - best anti ageing. A MUST if you use any acids, retinols, peels etc. Asian sunscreens are v popular as they're often a much lighter texture or gel.
Hydration: oily or dry, you're probably dehydrated. Add light layers of hydration with hydrating toners with Hyaluronic Acid, glycerin or panthenol. If you don't get on with HA, try something like Pyunkang Yul Essence Toner. Hydrating toners are very different from heavily astringent, stripping toners of yore.
If you're starting new products, I beg you to patch test and introduce products slowly, one by one. Don't overdo acids, retinoids/retinols etc. Do once a week and gently increase.
Azelaic Acid is a great start. Helpful with texture, acne, redness etc. This one is popular and silicone free.
Moisturisers: Clinique moisturise Surge, LRP Toleriane Ultra, Avène Skin Recovery cream. Possibilities are endless but generally better to avoid heavily fragranced.
Watch Gothamista on YouTube. Her videos from last year on hydrating toners, essences etc are good. Liah Yoo, Dr Sam Bunting etc