For moisturizer, during the day, I either use Neutrogena with SPF 35 (if I'll be outside), or Clinique Dramatically Different Moisturizing Lotion. At night I use Cera Ve PM; I have combination skin and some areas of very dry skin; this is what the dermatologist recommended and it's helped a lot. I've also really liked Aveeno Positively Radiant moisturizer, but it's pricey. This other combination is working for now.
For washing my face, I use something really mild, like a bar of Dove soap or Clinique little soaps. I can't use fancy cleansers or expensive cosmetics because for some reason they make my skin break out; especially around my eyes. I think it's the fragrances. I can't use products by Mary Kay, Lancome, Estee Lauder etc., although Clinique is fine.
Getting rid of sugar and dairy seems to have improved my skin too (yay!)
For shampoo/conditioner, I buy whatever "For color treated hair" formula is on sale or for which I have a coupon. Pantene, Dove, etc. My hair tends to be dry and I use a lot of conditioner. I like the Neutrogena mask that comes in a jar, and I use a little bit of leave-in conditioner too (Garnier Fructis). Leave-ins are hard to find!
You might want to try a clarifying shampoo, Neutrogena is one; or maybe add it into rotation a couple of times per week. They tend to strip your hair a bit more than the moisturizing shampoos. We always have some version on hand for our swimmers; as they are great at getting the chlorine out. There's a Suave kids' brand of swimmer shampoo that's clarifying but might be a bit milder, that you could try too; here it comes in an orange bottle.
My hairdresser also recommended going a few rounds with Ultraswim (another clarifying / anti-chlorine shampoo) when I accidentally colored my hair the wrong shade and needed to tone it down It helped fade the color faster.