What decides the choice
In the UK and the EU, cosmetics list their ingredients by standard INCI names, in descending order of quantity down to one per cent. That makes the first five or so ingredients the best guide to what a product mostly is. A serum that names an active ingredient on the front but lists it near the end of the label probably contains very little of it.
Many of the most common words on the front of a pack are not regulated definitions. Natural, clean and dermatologist approved can mean very different things from one brand to the next, so look for what the claim is based on. Animal testing for cosmetics is banned in the UK and the EU, but cruelty-free status also depends on where a brand sells its products and on its suppliers, which is why independent certification schemes exist.
Patch-test anything new before using it on your face, especially products with fragrance, essential oils or strong actives such as retinoids and acids. Check the period-after-opening symbol, an open jar with a number of months, because that is how long a product stays reliable once opened, and for skincare it is often shorter than the time it takes to finish it.