Prewash and dry them very thoroughly before you start cutting, because the cotton will shrink at a higher percentage than the batik. Because of the way batiks are produced, they will not shrink. Cottons will, and they will continue to have a small amount of residual shrinkage over the years.
Sorry if that sounds like a "rule", but I am assuming that you really don't want parts of your quilt to remain flat and smooth and other parts to shrink up.
Also, some of the batiks are heavily over-dyed. They may not fade at all in the wash, but they will bleed -- not just in that first wash where you can use a color-catcher, but also over time.
I prewash everything, but batik colors still bleed. I live in a fairly humid part of the country, and our red-and-white bed quilts show some of the results - even without additional washing, the edges of my white pieces are pink/red.
Believe it or not, the expensive batik fabrics bleed just as much or more than the cheap ones (especially the darker reds and greens,) which have been overdyed). Wash the heck out of them before you start.