Hi! <img src="/images/graemlins/smile.gif" alt="" />
You can quilt curves on a regular sewing machine, if it's not a really ancient one. You just need to get a darning foot (sometimes called a "hopping foot") for your machine. It allows you to do the loops, swirls, and curves that are called free motion quilting.
I'd recommend getting a few accessories for this type of quilting, such as gloves that have sticky-ish dots on the palms (so that it's easier to maneuver the quilt through the machine) and the clips that allow you to roll up the quilt on the sides that you aren't quilting at the time.
This is the kind of quilting I do the most of, and it's great fun <img src="/images/graemlins/smile.gif" alt="" /> I made pretty quilts for my daughters with quilted hearts <img src="/images/graemlins/smile.gif" alt="" /> You will probably want to make a "test" quilt, of two big scrap fabrics and batting, so that you can get the feel of what you are doing before you tackle your project. I like free motion quilting because you can quilt big (quick project, fluffier batting) or small (flatter project, cooler quilt).
Good luck with it, and have fun! <img src="/images/graemlins/smile.gif" alt="" />
~ Michelle.