I can't really help with the batting, because I don't know enough about the different types.
I have handquilted a gfg though! I used perle cotton thread and did big stitch quilting, because I didn't think I'd be able to get nice small stitches. I also did all the quilting 1/4" away from the seams (I marked them with 1/4" tape) which probably helped! I used cotton/bamboo wadding in mine.
Also, are you using a new needle? I've found that they blunt quite quickly, or get tarnished which makes it very difficult to pull through (never knew that before I did my gfg, I thought needles lasted forever! It was a bit like when you change your rotary blade and think "why did I not do this until now!") I'm piecing another hexie quilt atm and am using clover black gold needles, which have a special coating on them which helps them glide through a bit easier, don't know if they'd be any good for quilting, but I thought it might be worth a mention!