First, let's get the business of thread-painting out of the way. I can tell you what I use, but I heartily encourage suggestions.
With my thin thread, I use small needles. I like 75/11 or 80/12 sizes. I usually use Schmetz jeans/denim or Microtex. The shop where I purchased my machine suggested a new brand, Inspira. I have been using their denim and Microtex and sometimes their titanium-coated needles and they seem to work pretty well- they're cheaper too. I change my needles a lot. When they make that popping noise, it's time for a change. Sometimes I will notice nests or loops on the back -- time for a new or different needle. I don't change my machine tension a lot after I make my sample. Just the needle. When using thicker thread, a larger needle is in order -- without a lot of blather about technical stuff, I suggest 90/14 Topstitch needles.
As for fabric, I use anything I can lay my hands on. My favorite stuff to use is hand-dyed cotton, but I'm not proud. I'll use anything that suits the project.
Which brings me to stabilizers. I have been using Decor-Bond for a while now -- it's fairly lightweight and doesn't feel too crinkly inside of a quilted project. A friend (thanks, Robbie) recommended Sulky Totally Stable recently, so I'm going to be experimenting with that this month. I have a project that I abandoned because I didn't use any stabilizer before I started covering it with thread. I'm going to see if I can reclaim it with stabilizer.
And don't forget feet: I use my freemotion foot with the feed dogs down. Sometimes I forget and leave them up -- I usually don't notice until I remove the piece. So I'm not sure it's all that important.
Next: thread-sketching and the value of making samples