It's less to do with brands as ingredients. I'd suggest watching some of Nadine Baggott videos. She's fab, and explains the science behind ingredients and what they do in a very simple way. She also doesn't go in for the "you need 28 different products" thing that others do
You need:
A cleanser/make up remover. You don't need to spend a lot on these as they go down the plughole after 30 seconds. I love Liz Earle and I also like Superdrug Vit E. Superdrug do a "radiant" one supposedly a dupe of LE but I didn't get on with that.
A vit C serum in the morning, will brighten. (Must use sunscreen after)
A hydrating serum
A moisturizer that's suitable for your skin. I love some high end ones (L'Occitane Divine for example) and Liz Earle Superskin, but tend to buy whichever L'Oréal/Olay/Garnier is on offer. Again, you don't really need to spend on moisturizer.
An acid toner, glycolic for dry, salicylic for oily. These have replaced the hideous gritty things we used as teenagers and simply exfoliate dead cells away.
That's it really.
I don't stay loyal to brands and I don't buy into the Ordinary style philosophy of having 20 single ingredient products at a fiver each when I can have one more expensive product containing everything.
Superdrug do great skincare. One of my favourite serums is Superdrug Simply range which costs about £4.
Boots N7 do great skincare, and you need to remember Boots is massive and has a huge research and development section going on which means often their products are pretty cutting edge. I buy the Lift and Luminate range when it's on offer.
Liz Earle, Clarins and Clinique all have good rep for skincare. If you're sensitive you might react to the essential oils/perfumes though. Don't fall for the "Simple" name and brand. It's really not!
La Roche Posay Toleriane is for sensitive skin. Cerave is another highly recommended brand.