I agree 100% about starting slow and giving each product you add to your routine at least a week to see how it works for you--obviously if it starts burning or you get an allergic reaction stop it right away and take some Benadryl.
If if you don't yet have a cleaner you like, here are a couple of different formulas that people with sensitive skin swear by.
Drug store Cleansers: (both recommended by dermatologist to people looking for so,etching basic and cheap that works for sensitive skin)
Cetaphil isprobably the most popular of the two, a lot of users started with it in their teen years and then found it continued to work well for them as they aged. Neither this nor CeraVe is my favorite because I think they have a slightly odd scent that reminds of cold cream and it bugs, but for the $$ you won't find better.
Slightly higher end cleansers-- think Ulta, Sephora or somewhere online like
Drunk Elephant--both their Jelly cleanser and their Pekee bar are well liked, limited ingredient, nondrying choices
Korres--they have several options but I personally love the Goats milk foaming cleanser because I don't have to double wash and it's enough to remove even my waterproof mascara without leaving my super sensitive skin irritated or dry. I know both Korres and DEs options are more, but you probably only need to replace the jelly or cream versions once to twice a year.
Cheap Moisturizers-- target, Whole Foods, Amazon are the best priced options
Accure's Argan Oil--just like the more expensive versions you'll sometimes see in Sephora, this is 100% organic and free of additives. In theroy over time it'll help your skin cope better with things that irritate it. What I've noticed is that it does an amazing job of keeping my skin balanced, soothes reactions from new products I try and end up reacting to, and results in my face being a great canvas for makeup. Depending on how dry my skin is I either use it both at night and in the morning before makeup or just in the morning. If it's not enough moisture on its own, put it on before bed and let it sit for a few min before putting on a layer of moisturizing cream on top. Also Argan oil is supposedly the most efficient way for your skin to absorb vitamin E, so it's a good anti aging choice if you're worried about that at all.
Cetaphil-- has a moisturizer too, some like it, some hate it.
Olay-- they have several lines for sensitive skin so pick which ever addresses your concerns.
Higher End Moisturizers
Drunk Elephant's B Hydra Serum--it's fantastic, my mother even likes it better then her old Chanel hydra serum, and it's among the more effective moisturing serums on the market.
Drunk Elephants LaLa Cream-- a super think cream moisturizer that's great for just slathering o your face when it's chapped from the weather or dry from too much AC or heat exposure.
Sunday Rileys Oils--you can't really get an equivalent elsewhere and people at Sephora can make up a sample for you to try for whichever will work with your skin. Be sure to test a patch on the back of your neck then wait a few mins to make sure you won't react before putting it on your face. Some people with sensitive skin find it too much, for others it's just right.
Holy Snails-- it's an Indy that sells online only,but you might find you really liked the Vitamin C oil and/or her hydration Serum and you can testers of either online. If you liked them their both at least slightly cheaper than most DE stuff and lost cheaper than other brands.
My last recommendation is that if your not sure of exactly what your skin is reacting to or what is making it so sensitive then you should consider stick to lines like Drunk Elephant which doesn't add any extras like fillers or fragrances to limit what's going your skin and what you might react to. Happy hunting!