I think I just about burned my skin off with various acne medications when I was a teen/20s, so I'm not sensitive, but what I use is inexpensive:
Face wash: Target baby wash - it's what my kids use, and they have super sensitive skin. I just use it in the shower with a washcloth.
I alternate these so each one is used every 3rd day:
Coconut oil (giant tub from Costco, but I prefer the Trader Joe's smell)
Amlactin (super cheap from Costco and a little goes a long way!)
Retin A .025% ($20 when I can get dermotologist to prescribe it for acne) - this is a super low concentration so it doesn't cause redness/flaking - on me at least.
With a good diet though, I think you can get away with using anything. I eat mostly whole foods, drink lots of water, and take loads of magnesium, niacin, fish oil, and Vit C every day.