Are you hand-piecing, or hand-quilting, or both? I have not hand-pieced a quilt, but I would suggest that you iron a fold for your seam-allowance, or mark a line with a fabric pencil, and then do a sort of "running back stitch" if you know what I mean. Sewing in a straight line, make a stitch forward, and then the next stitch, bring your needle up through the cloth farther away, and then back down where the last stitch ended. Do the same with the next stitch. This way, the thread overlaps on the underside of your work, and makes a good strong stitch. (this is sounding really complicated. I wish I could make a diagram for you. Just let me know if you can't visualize what I am saying, I'll try to explain it better!) Also, get thread for hand quilting, it will stand up much better to being pulled through the cloth repeatedly. Other thread will fray and break.

I don't know whether you need a frame for hand piecing. You will want one for hand-quilting. A large hoop has worked fine for me - makes it easy to work with on your lap.

HTH!
All the best with your project!