It depends on what type of silk it is. If it's dupioni, which is somewhat thick, it doesn't need a stabilizer. If it's Charmeuse, which is quite slippery, you may want a very thin interfacing on it. However, I would hesitate to use an iron on interfacing even if it is slippery silk... silk needs extremely low heat. High heat ruins it. It's also sensitive to water... it can leave water spots as it dries. Since many interfacings need steam and high heat to adhere, that would put me on high alert. And you say it's painted too... so it's unknown if the paint can be heated also.
So I think I'd NOT use any iron on product on it. If you want, you can use a thin fabric layer behind it. Either a Sew In Interfacing or muslin which you'd just baste to the seam allowance edges to add body. Also, your outer pieced blocks will act as a stabilizer of sorts too, in that it will hold the edges square and flat. Be sure to use a larger seam allowance than 1/4" if you see that your silk is unraveling easily.
As for quilting, silk quilts beautifully. Use the smallest size needle you can and still get nice stitches and no thread breaks. On a longarm, I'd suggest a size 16. On a DSM, perhaps an 11 or even a 9, if you can. You have to test first. I would not mark the quilt because it might be hard to get the marks out. For thread, any thin thread would be nice. So Fine, Aurifil 50 Cotton Mako, Masterpiece or even Silk thread. If the piece is shiny, then perhaps a shiny poly like Isacord would look nice.
Batting, again, whatever you like. I'd just stay away from super fluffy scratchy poly from the big box store. I love Quilters Dream Battings, so I might use their cotton or blend or poly (which is very soft).
HTH... please post a picture when it's done!
