there are different broadclothes...some are cotton/poly blends, some are just poly and some are just cotton...i have used many cotton broadclothes in my quilting...and a few blends. there are different weights too...find one that is about the same weight as the other fabrics in your quilt.
as for batting there are as many answeres as there are batts...all have their place and you will have to try some and decide what you like. one of the most important parts of choosing a batt is to check to see what the quilting recommendations are...some batts you have to quilt every 2" (very heavily quilted) while some you can have up to 10" between stitching lines...so that needs to be taken into account. cotton batts shrink a little, are nice to work with, tend to stay pretty flat...poly batts are great to work with and hold up very well, especially good in kids quilts that will take a beating. wool batts have wonderful loft are soft and fluffy and a dream to work with...and on the higher price end. there are plenty of specialty batts also. some people use fleece or fusable batts too...read packages and try what you can afford that seems to meet your needs....there is special batting for potholders.