I use size 12 Betweens needles. John James brand is good...so is EZ brand from JoAnn Fabrics.
When I learned to hand quilt, my teacher made us use size 12 Betweens and practice, practice, practice our hand quilting skills. I'm so glad that she did, because after a week of practice, my stitches were small and even. She showed us how to use one of those metals thimbles with the brass ridge on top, and do the rocking motion. I practiced by making a white-on-white pillow top.
If I use muslin for the backing, my stitches on the front look good, and my stitches are small and even. When I've used a cotton print, or solid, for the backing, my stitches look bad.....and I had LOTS of trouble getting the needle through the quilt sandwich. I abandoned an Amish wall hanging because I'd basted a cotton solid on the back instead of muslin. It was agony trying to hand-quilt it! Also, smooth, not lumpy, polyester batting is easier to hand-quilt through.
So, you might want to try using muslin for the backing, size 12 Between needles, and good quality, thin, 100% polyester batting (like Hobbs or Mountain Mist) and see how these affect your hand quilting.