@cbrande, my skin is dehydrated-combo leaning dry and I deal with breakouts periodically as well. If you are looking at clean skincare, brands like Drunk Elephant, Tatcha, Farmacy, Tarte and the Sephora Collection are good ones worth looking into.
SKINCARE
With skincare, you'll want to slowly introduce products into your routine and use it for some time (unless it's causing you irritation) to see how your skin responds to it. Some clean skincare products that you might be interested in include:
Cleansers - I double cleanse at night and like to use either Tatcha The Camellia Oil 2-in-1 Makeup Remover & Cleanser 5.1 oz/ 150 mL or Farmacy Green Clean Makeup Removing Cleansing Balm 3.4 oz/ 100 mL as a first cleanse. For a good clean beauty second cleanser, try SEPHORA COLLECTION Clean Skin Gel Cleanser with Prebiotics or OLEHENRIKSEN Truth Juice™ Daily Cleanser 5.0 oz/ 148 mL. Sephora Collection has a set available that would be a good starter set - SEPHORA COLLECTION - The Essentials Kit.
Exfoliating once or twice per week is great and there are several chemical and physical exfoliants out there to choose from. Some clean options include: for chemical exfoliants, either FIRST AID BEAUTY - Facial Radiance Pads or SEPHORA COLLECTION - Glow Peel Pads, both are gentle on the skin. TATCHA - The Rice Polish Foaming Enzyme Powder is a good physical exfoliants; there are different formulae available depending on your skin type.
For moisturizer, it depends on your preference for textures but there are a lot of options out there as well. If you have very dry skin, Drunk Elephant Lala Retro™ Nourishing Whipped Refillable Moisturizer 1.69 oz/ 50 mLis great. Mixing in a drop of a moisturizing face oil is also great for very dry skin and tarte Mini Maracuja Oil 0.5 oz/ 15 mL or Drunk Elephant Mini Virgin Marula Luxury Face Oil 0.5 oz/ 15 mL are worth looking into. If your skin is dry but not very, very dry, you might like something with a lighter consistency like Drunk Elephant Protini™ Polypeptide Firming Refillable Moisturizer 1.69 oz/ 50 mL or the moisturizer in the Sephora Collections Essentials Kit.
Supergoop! Unseen Sunscreen Invisible Broad Spectrum SPF 40 PA +++ 1.7 oz/ 50 mL is a great sunblock from a clean brand; it works well for me when I'm dry as well as when my skin is more combination (oily T-zone). It doesn't cause me any breakouts either.
"Extras" as far as skincare goes for your skin type and concerns include:
MAKEUP - I've been liking KOSAS - Tinted Face Oil Foundation for a clean base product. Tarte, Cover FX and RMS have a good selection of clean beauty products that are worth checking out. There's also a section on Sephora online under the "Makeup" tab for "Clean Beauty" that'll make it easier to identify the clean beauty products.
HAIR CARE
I've gotten good results from all the Briogeo and Olaplex products I've used. Olaplex No. 3 Hair Repair Perfector 3.3 oz / 100 mL, Olaplex No. 4 Bond Maintenance™ Shampoo 8.5 oz/ 250 mL and Olaplex No. 5 Bond Maintenance™ Conditioner 8.5 oz/ 250 mL have all be repurchased and gifted by me. Briogeo Don't Despair, Repair!™ Deep Conditioning Hair Mask 8 oz/ 237 mL is one of my go to hair masks. Their Briogeo Superfoods Banana + Coconut Nourishing Shampoo + Conditioner Duo for Dry Hair is also a nice one - love the smell too.
If you are near a Sephora store, you might want to see if you can get samples of a few of these items to try out before committing to a full size.