There are many, many types and brands of quilt batting on today's market.  Unfortunately, no single batting is the best choice for every project.  Basically, there are three types of fiber content found in batting:  cotton, polyester, and wool.  Each type is appropriate for different looks and purposes. 

The majority of quilters use either polyester or cotton batts.  Batting comes in many thicknesses called "loft."  If you are new to hand quilting, I recommend using either a low-loft or medium-loft batting.  It makes the quilting stitch much easier to learn.  For machine quilting I have found that 100% cotton batting seems to work best as the quilt top and backing do not shift as much as they do when using a synthetic batting. 

Make sure your batting is made by a reputable company as inexpensive brands are sometimes uneven in loft thicknesses and not properly treated.  I encourage you to read the product information included on batting packages.  The more you understand about the differences in battings the better decisions you will be able to make for your quilts.  

BATTING SIZES:  Standard batting sizes are:

Craft        36" x 45"                 Full            81" x 96"
Crib          45" x 60"                 Queen      90" x 108"
Twin         72" x 90"                 King        120" x 120"

     Rolled batting by the yard:  45", 48" and 90" widths

PIECING BATTINGS:  Battings come in various sizes, but sometimes you need a larger size than is available in a particular brand.  This is when you need to splice two batts together to get the needed size.  The quickest (and easiest) way to do this is to butt (not overlap) two even straight edges together and whip-stitch the seam.  Do not pull tight the stitches as this will create a ridge in the batting.  An overcast stitch (stitching in the same place several times) will reinforce the beginning and end of the seam.

Note:  Piecing the batting is a good way to use up leftover strips of batting from previous projects.  However, I generally do not piece battings for bed quilts (when possible) and limit the practice to wallhangings as they will not get the wear that a bed quilt would receive over the years.