Not sure about batting..have no idea the differences or best

Blue painter's tape, as wide as you can find. I use this in multiple ways; this is just one. Roll the tape around your hand a couple of times, sticky side out, and adhere to a convenient surface as a thread catcher. Just touch threads to it and they stick. When filled, toss and make another.

Elmer's white washable school glue. You may find this works better than pins for matching intersections when piecing, and for applying binding.

Seam ripper. I like the small, inexpensive, blue Dritz seam ripper.

Dritz adhesive seam guide refills (JoAnn's might have them) or, if you can't find that, the thickest moleskin you can find in the foot section of a pharmacy. I use these to create a physical barrier for my 1/4" seams. (Jan's above is another way to do this.) Here is a link to the Dritz refills I like best:
http://www.amazon.com/Dritz-Quilting...dp/B0085L2Y2I/

You can wait on batting. A good one to start with is Hobbs 80/20 (80% cotton/20% poly). If you like vintage style quilts then you will want to go to 100% cotton. If you prefer fluffier quilts, you will want to try out the polys. But 80/20 is a good starting point.

Edit: Oh, yes, and at least one can of the best spray starch you can find. Later on, for the backing fabric, you may also want to purchase a quarter of Sta-Flo liquid laundry starch; but that can wait.

Rotary cutter and mat.

ruler/s to go with the mat and rotary cutter

I've taught a lady here how to make tops and you really only need fabric, pattern, mat, cutter, ruler and seam ripper, scissors, plus thread of course and the sewing machine.

All the rest are extras in my opinion.

Of course, when you get close to the end you need your batting.

Also you need access to an iron and an ironing board or mat of some kind.

I love my June Tailor's Shape Cut rulers, a 1/4 inch with guide. These 2 items will really help with your accuracy.

Buy what you need for the first quilt and with the next quilt you will add to your tools what you don't have that will make the process easier. You'll find out the smaller cutting mat is too small, the ruler is either not long enough or too long, the scissors aren't that sharp, the batting is too puffy, and that thread is sure linty.

If you are planning a QAYG, you will need the batting up front along with the fabric (it all goes together at the same step)

A ruler to use with the cutting mat and rotary cutter.

Measure twice, cut once.

Nevertheless, I always buy more fabric than called for in the pattern.

You don't want to make a major booboo and find that the needed fabric isn't anywhere to be found. Extra fabric can join your stash: you'll have favorite fabrics to make a scrappy quilt down the line. :)

I didn't have for my first quilt, but I bought soon after......a 1/4 inch foot for my machine. So no more guessing about seams. Other than that I have not really invested in too many gadgets. Purchased a large mat, rotary cutter and ruler as a set at Joanne's with a 50% off coupon and free shipping. To be honest I have used thin blankets for my batting so far at $5 each and the quilts feel fine (only 4 completed). I think back to my grandmother and they didn't really have much to work with so I don't stress that part. I have not done a QAYG yet, but soon maybe.