I will replace fabric provided in kits with a larger piece or different color to suit my taste. I will also change the count of threads in a fabric to change the look of the final stitched piece. My preferred fabric is 16 count, which is 16 threads/holes per inch. If I want an even smoother finish I will use 18 count fabric. I just purchased two kits with fabric measuring over 36 inches; if I use the 14 count aida provided. I don't want the finished pieces to be that large, nor do I want to worry about running out of thread. I will be stitching them both on 18 count fabric.
Not all designs are suitable for a hand dyed fabric. I generally do a floss toss before making my final decision. I like neutral fabrics for any design that contains wording.