I agree that you need to tape the backing to the floor or other hard surface, not the carpet. Use quilter's safety pins and pin about every 4 inches. After you have it pinned, flip it over to check for any wrinkles before you start quilting. You may need to re-pin. Test your quilting stitch first on a test 'quilt sandwich' which is just 2 pieces of fabric and batting similar to the quilt on which you will be quilting. You may need to adjust your tensions if the stitches are off. What type of batting are you using?
I do donation quilts and have done about 2000 for various organizations. You can spray baste and then wash the quilt after you have finished quilting. Be aware that a lot of the basting sprays are temporary and only last a day or two. If using a basting spray, try to use the non-toxic ones.
Make certain there is no drag on your quilt when quilting. You may need to 'toss' it over your shoulder to take any weight off or it can affect your stitches.
I do mainly free motion quilting, but have stitched in the ditch on some of the quilts. I also like to use the 3 step zig zag on the binding. If you are doing a quilt for preemies, check with the organization. Some hospitals do not want any batting used and want those quilts backed with flannel and minimal if any quilting- just around the edge. Preemies skins are very fragile.
A walking foot helps in 'stitching' in the ditch to keep the layers even, although I like meandering (free motion quilting).
Also, what type of thread are you using? I use a bobbin weight thread mainly. The needle is important also. Here is a tip on needles from Superior Threads:
for 60 wt., monofilament, and #100 threads: use a #70/10 Topstitch needle
- for 50 wt. threads (piecing wt. threads): use a #80/12 Topstitch needle
- for 40 wt. threads (quilting and embroidery): use a #90/14 Topstitch needle
- for 30 wt. and heavier threads: use a #100/16 Topstitch needle
Here is another tip from them regarding thread type when quilting. Quilting King Tut (cotton), So Fine #30, So Fine #50 (poly), Rainbows (high sheen variegated), OMNI, Silk, Highlights, Art Studio Colors, Nature Colors, Living Colors, MonoPoly, Poly Quilter, Lava
Of course these are their threads. Some threads don't always work on all machines. Thus, it is important to test first. I do use a titanium needle and have used a variety of threads. How old are your threads? They do deteriorate over time and especially if exposed to dust.
Hopefully this is not TMI.
Good Luck