It's not that complicated.
J&J baby shampoo (which you can usually get in a travel sized bottle) works well for this, as does any of the VO5 Herbal Escapes or Suave Naturals shampoos.
Just a silicone-free regular conditioner is fine. In summer, most of us don't need anything all that rich, in winter it helps to use something that's more emollient.
A deep conditioner is different. It is most emollient, left on for an extended period of time, and usually used with heat.
Since I started using the new Curly Girl method, which has you just throw a couple of handsful of water at your hair (called a trickle or Baptismal rinse), I haven't needed to use a separate leave in. I never imagined my hair would tolerate this much conditioner, but without the silicone coating, it doesn't get weighed down or look like I encountered an oil slick.
Some of us use a curl cream, but it's not required. What Lorraine Massey does say, though, is to use a silicone-free gel. Prior to going CG, in addition to having thought my hair couldn't tolerate conditioner, I hated gel because it always seemed to coat my hair and make it hard. What I didn't realise was that it wasn't gel I hated, but gel with silicone. Without the silicone, you can easily break the gel cast (the hard casing around your hair which protects your curls as they dry) once it dries, by simply scrunching your hair, and it falls off.
You're right about the sulfate and silicone free part. The fancy smancy towel, not so much. You may get one if you wish, but you can use anything absorbent with a smooth surface. I used old dish towels at first. Then I moved on to old T-shirts. (If you have a serger, you can make your old T-shirts fancy by cutting off the body, and giving it a lettuce edging.)