If you use a longarm machine with a frame, you need to load the backing, batting and top onto the frame. If the machine is a table machine (the kind most of us use at home), you need to baste the three layers of the quilt sandwich before you start quilting on the machine.
If you are going to machine quilt on a regular machine, I highly recommend spray basting. It is much, much faster than other methods (traditional hand basting with thread and needle, basting with safety pins, or even basting with a basting gun -- similar to how price tags are attached to garments). You can buy basting spray at JoAnn's and sometimes places like Walmart. 504 is probably the best brand, if you can find it, but all of the other brands will work too. Just be sure that you use it in a very well-ventilated area; some of the brands smell pretty toxic and you don't want to be breathing in spray.
Spray basting works best with cotton battings, although many people also use it successfully with polyester batting. I personally prefer a very traditional cotton batting (Mountain Mist Blue Ribbon). I also heavily starch my backing fabrics so they are quite stiff. This helps me prevent unwanted puckers underneath while I am machine quilting. If you want my methodology for starching the back, I will write it up in a separate post.
Whether you use cotton batting or polyester batting, you will be much happier if you stay away from high-loft batting. Low-loft battings are much easier to machine quilt.
Are you planning to stitch straight lines, wavy lines, or free motion? I think the easiest are wavy lines using a walking foot.
Oh, and to answer one of your questions more clearly -- usually you layer the quilt sandwich and baste it, then machine quilt it, then add the binding last. Binding is an entire subject by itself! It's also possible to do a "pillowcase" edge where you layer the sandwich wrong sides out, sew around the edges leaving an opening, then turn right side out, sew up the opening, and quilt; however, this is usually used for smaller quilts like crib and lap sizes.