Prism99

It sounds as if you are basting using some combination of pins and glue. Try switching to spray basting or glue basting. With spray basting, all three layers are continuously "glued" to each other. This minimizes how much the fabric can stretch while you are quilting. Glue basting is similar.

Also, heavily starching your backing and quilt top should help. Puckers are caused by the fabric stretching as it is quilted. This becomes particularly noticeable when you cross other quilting lines; there is excess fabric bunched up right next to the line you have to cross, requiring a tuck. Starching minimizes this issue because it stabilizes fabric and prevents it from stretching so much.

For backing fabric I like to use a 1:1 solution of Sta-Flo liquid laundry starch and water. My fast method of applying this is to "paint" it on the fabric using a large wall painting brush, waiting a few minutes to make sure the fabric has a chance to absorb the starch, tossing in the dryer, and ironing with steam. Steam reactivates dried starch.

For the top, multiple layers of spray starch can be used. Lay the top out on a large flat sheet and spray from the edges towards the center to minimize overspray. A fan can be used to hasten drying time between layers. For a quilt that has already been basted, you can use this technique on both the top and backing layers to stabilize them.

On some machines you can lessen the pressure on the presser foot. This also can help, especially if you are using a thicker batting.

You may be misunderstanding how to layer a quilt. Honestly, tautness is not an issue. What you want is a smooth backing, not a taut backing. If you stretch your backing fabric (for example, by stretching the fabric taut and then taping the edges to keep it taut), it will spring back to a normal tension as soon as you untape. If you have already basted, this adds fullness to the backing fabric and you are more likely to get puckers and tucks in the backing when you quilt. If spray basting or glue basting, you "smooth" each layer as you go. A yardstick is handy for smoothing out wrinkles and lumps. That's all. No tautness; just smoothness.

What batting are you using? A thick polyester batting is the hardest to quilt. Hobbs 80/20 is a good starter batting that has some loft, but not so much that machine quilting becomes difficult.