oily skin can be so annoying! i've had oily skin pretty much forever. previously, it was dehydrated which just made the oil even WORSE, however even now when my moisture barrier is in tip-top shape, i'm still pretty oily.
pH balanced cleansers are one of the most important things to me. the second i start using a high pH cleanser, or something that lathers way too much, my oily skin goes into overdrive. bioderma sensibio micellar water, simple moisturising wash, la roche posay dermo cleanser, la roche posay micellar water for reactionary skins are some of my favorites.
a BHA is awesome! i love stridex ($8AUD) - it's a bit harsh but now that my acne is gone away, i only use it ever 3-4 days. i find it definitely helps with my oily skin and i can notice a difference in my oil production if i slack off using it.
using rich moisturisers and oils in the PM also help me a lot. my skin is very prone to getting dehydrated - so i try to keep on top of that. embroylisse lait creme concentrate ($29AUD), la roche posay toleriane rich ($29 AUD), rosehip oil ($8AUD) and shea butter ($13AUD) work amazing for me. they keep my skin smooth, moisturised but not overly greasy to the point i'm uncomfortable.
i've found in warmer months, i don't use moisturiser in the am - i just use a gentle cleanser/micellar water -> rosewater -> sunscreen. this really keeps my face a lot less greasy throughout the day, and because my skin is naturally oily the sunscreen provides enough moisture for the day and then at night i slather my skin in rich moisturisers and oils.
finding sunscreens has been tough, so far my two favorites are the biore watery essence ($20AUD 2-pack) and the la roche posay antheolios ultra light ($28AUD) - they're both light, lotion type textures that sink straight into my skin with no residue. alcohol denat is high up in the ingredient list if that's a concern for you, however it has not been an issue for me.
blotting sheets are a must - you can get them in all different stores or online for pretty cheap. i find most brands work about the same and in summer they're an essential for me.
overall, i find being gentle to my oily skin keeps it in best condition. i'm always trying and testing new products, since i have lots of friends and family in the beauty industry (so i get a ton of samples all the time, plus i always go and get my own samples too), so my recommendations are constantly shifting.