Nothing here is expensive, and none of it is essential in the specific — a cheaper equivalent in the same category does the same job. The category matters; the brand mostly doesn't. Links below are affiliate links.
SunscreenThe one that matters
Beauty of Joseon Relief Sun SPF50+ PA++++. A light, non-chalky finish, which is the only reason anyone applies enough of it. If a sunscreen feels bad you will under-apply it, and an under-applied SPF 50 performs like an SPF 15.
Alternate: La Roche-Posay Anthelios UV Clear SPF 46 if you're acne-prone.
MoisturiserThe load-bearing one
CeraVe Moisturizing Cream. Ceramides and a tub that lasts months. This is the product that makes 0.1% tretinoin survivable, and the one I'd replace last.
Alternate: Vanicream Moisturizing Cream — same job, shorter ingredient list, no fragrance.
Hyaluronic acidCheap leverage
The Ordinary Hyaluronic Acid 2% + B5. A few pounds, lasts forever, and does exactly one thing. Damp skin, then seal — otherwise don't bother with it at all.
TonerHydrating, not stripping
Klairs Supple Preparation Unscented Toner. No alcohol, no fragrance, no witch hazel. Its only job is leaving the face damp for the hyaluronic acid. Anything marketed as "clarifying" or "pore-tightening" is the wrong category for skin on a retinoid.
Face wash — oilFirst at night
DHC Deep Cleansing Oil. Dry hands, dry face, one minute, then emulsify with water. This is what actually removes a water-resistant sunscreen. Skipping it is why people who "wash their face properly" still get congestion.
Face wash — foamSecond at night
CeraVe Foaming Facial Cleanser. Takes off the oil cleanser without stripping. Lukewarm water, thirty seconds. If your face feels squeaky afterwards, the cleanser is too harsh — squeaky is damage, not clean.
Tretinoin 0.1%Prescription only
No link, because there shouldn't be one. Tretinoin is prescription-only in the US and anywhere selling it to you without one is selling you something you can't verify. Get it from a dermatologist, a GP, or a legitimate telehealth service that actually prescribes.
If 0.1% is more than your face wants, 0.025% and 0.05% exist and are not a lesser version of the project.