I think something else to consider is that even though it's great you're helping her to start up a routine, she needs to think caring for her skin is a priority. Of course not everyone needs to be as interested/invested in it as we are, but if she wants to heal her current problems as well as take better care of it in the long term, she should to be informed about the basics of how and why to use certain products. If she has problematic skin, it often requires work, and if she wants to get it to a better place, knowledge is her best tool (as it usually is for most problems). Even if you get her every amazing product on the market, it won't help at all if she's not going to care about them enough to use them properly! I think people often forget that the skin is an organ just like our lungs, kidneys, livers, etc. It's not just a cosmetic or vanity issue, it's a health mandate to take care of ourselves!
So maybe she's inspired to start a routine now, and of course she is free to make her own decisions about what to use or not to use, but if she's serious about fixing her current problems then yes, she should approach both the research and the routine with a degree of commitment.
Now with that said, onto my product recommendations and general suggestions! You probably already know much of this since you've been AB for a year, but I'll type it all out anyways. As someone who has a very similar skin history/type as your sister, these are the things which helped me:
a good oil cleanser. I LOVE the banila co Clean It Zero but some people react very badly to it. I've also used The Face Shop Bright Rice Water Cleansing Oil (Light) and Hada Labo Gokujyun Cleansing Oil, they're both okay but not as thorough or pleasant to use as the Clean It Zero.
stop using foaming cleansers. For a long time I still double cleansed, but you know what? A month ago I raised my standards for a cleansing oil because if it's good enough, why do I need to double cleanse? I'm sure some people will disagree with me, but personally my face became much less oily and more balanced without any foaming cleanser (yes, even the pH appropriate ones without harsh ingredients). I didn't suffer from using a foaming cleanser, but things are better for me without. Finding an oil cleanser which rinses completely clean is KEY.
Vitamin C serums have made the overall biggest improvement in decreasing my scars and reducing pore size appearance. I currently use OST C20 but it's been pointed out multiple times that the formulation is not the greatest. Going to try SkinActives Vitamin C serum when I'm done with my current bottle of OST.
COSRX BHA Returning A-Sol or Paula's Choice 2% BHA Liquid. Might take a few weeks to see real results, but helps so much against future breakouts.
if she lives in the USA, seriously consider a Pocketderm prescription. Huge gamechanger for me. My prescription had niacinmide, clindamycin, and azalaic acid. Took 2 months to start seeing changing, but by the end of month 3 I looked soooo much better.
Benton High Content Snail Bee Essence didn't do much for my active acne, but it is so great for reducing inflammation and irritation anywhere on my body. Good for those "oh my god what do I do, everything feels terrible" moments. I even randomly used it on a weird allergy rash on my hand once, and IT FELT AMAZING and so soothing, itching gone within seconds.
DO NOT FEAR THE MOISTURIZER. Most of us know this, but new initiates of the oily-skinned variety often need to overcome this mental divide. Pick something very nourishing, perhaps even a balanced facial oil. I love Benton Steam Cream, Mizon Returning Starfish, pretty much anything from Kiehl's, and I've never met an oil that I didn't like!