It's not just the size you need to consider, but the type of needle.
I haven't worked with paint, but I am thinking you still need to stay up in the range of a 12 or 14 needle to have the "strength" to go through fabric plus paint.
The sharpness of your needle comes from the type of the needle.
My first thought would be an Embroidery or perhaps a Microtex needle.
Even with all the advice and suggestions you will get from everyone here, I would still recommend you have a sample piece to practice on.
Even if someone else has used the same paints, all will not be the same.
You will have used different fabrics, different thickness of the applied paint, different battings, different threads, different machine, etc. ..... so definitely do some practice work before you go for the real thing.