I didn't think you were being dismissive! I got that you were trying to say that you don't have a "fancy" or a very deliberate routine!
Okay, I think all the Suave Professionals stuff have cones in them so you're best to ditch them BUT you'll need to do one last wash to get rid of the silicones with a shampoo that doesn't
have silicones. So not the Suave shampoo, because that will add more silicones while breaking down others.
You can use a clarifying low-poo like Giovanni Tea Tree Triple Treat. I'm sure there are others I just don't know. You need a silicone-free low poo that has coco betaine or cocamidopropyl betaine in it to break down the cones. A cone-free sulfate shampoo will work too. And that's the last time you'll ever need to use sulfates!
If you want to go to low-poo route there's many that are popular: SheaMoisture, Yes to Cucumbers, Curl Junkie Gentle Cleansing etc. If you want to cowash, try the Suave Naturals or Tresemme Naturals conditioners. Or V05. Just double check whatever light conditioner you use to cowash has no silicones in it (ending in -xane, -cone, -conol). PEG in front means water soluble, which should be okay but some curlies avoid these as well.
I second getting a really moisturizing conditioner like GVP Conditioning Balm (knock off Matrix Biolage Conditioning balm). Your hair will most likely highly benefit from a leave-in conditioner as well. This can be the same as your rinse-out conditioner. The only thing I would suggest is avoid glycerin in leave-in and styling products if you live in an area with high dews. (You can check the dews on NaturallyCurly's Frizz Forecast
Weekly deep treatments will be a savior especially in the beginning. I use extra virgin coconut oil on my hair. Now since my hair is very moisturized and in good condition (and the dews are high), I've been using protein treatments more frequently. I use IAgirl's gelatin recipe for PT and this has really improved my hair. How much protein you need will depend on your specific hair properties.
Definitely figure out your hair properties! If you have trouble you can also get a hair analysis from Live Curly Live Free or Komaza Care! That will be so helpful in the beginning as you start to make changes and choose different products!