Most people on the skin care threads have a basic routine like this.
AM.
Cleanse with gentle water based cleanser or just massage with warm water (not hot).
Vitamin C Serum (the one every one was using is no longer available so there's a hunt on for a new reasonably priced one)
Moisturiser
SPF (sufficient quantity - I go with 2.5 ml for face and neck)
PM
Double cleanse. First using an oil or balm cleanser to dissolve makeup (if any) and SPF, second using a gentle water based cleanser to make sure all the oil and impurities are gone.
A retinoid or an exfoliating acid.
Moisturiser.
Retinoids include retinol, retinal and tretinoin (prescription only) and are forms of vitamin A. Anti-aging. Irritating and increase skin sensitivity to UV light.
Exfoliating acids (AHA, BHA and PHA) help get rid of old skin cells. Can be irritating and also increase sensitivity to UV light. AHAs are glycolic and lactic, BHA is salicylic and PHA normally called PHA. Glycolic is the most harsh.
Vitamin C - L- ascorbic acid in percentages of 10 or above. Improves collagen production, pigmentation, and glow. Unstable and can cause irritation and oxidise on your skin.
Other products - niacinamide, and lately tranexamic acid. The latter is for pigmentation. The former is vitamin b3 and is good for skin health, balancing oil production, and maybe anti-aging properties.
Most of the chat on the skincare threads are which products are a combination of the best value and actually work without being too harsh and irritating.
CeraVe cleansers and moisturisers are popular as inexpensive products that do the job nicely. Avene for sensitive skin and La Roche Posay Toleraine are a bit more expensive but not outrageous.
Paula's choice is good for BHA - the one mentioned above, skin perfecting liquid.
Medik8 is good for retinol and retinal and Avene also do a retinal. La Roche Posay do Redermic and there's a product from Indeed Labs called resurface that's quite good (it contains peptides - another anti-aging ingredient which may or may not do much but do cause increased hair health for me which is not what I want on my face). Tretinoin is available from online dermatology services Dermatica and Skin and Me.
It's best to introduce new products at least 2 months or so apart. Impossible to tell what is doing you good or causing harm if you start them together, and there's more chance of causing irritation.
The aim is to get your skin into balance and keep it there. Usually this is by by using the gentlest of cleansers and following with moisturiser with a possible hydrating serum step (your hyaluronic acid above) before the moisturiser. People might have 2 or 3 different moisturisers for times their skin is drier, more sensitive or it's winter. Or use an oil in addition to moisturiser. Your skin naturally has its own barrier to keep it happy and the aim is to help it rather than make it work harder (as far as I can figure out the only thing it can do is produce more oil). The balance of micro organisms on your skin is another thing not to be messed with. Skin is also at a certain pH.
Soap, shower gel, face washes (depends on what's in them) scrubs can all have a disruptive effect on your skin barrier.
My skin cleared right up when I started cleaning it properly.