I'd suggest a rotary cutter, a cutting mat, iron & ironing board. As you gain experience and get a sense of what kind of quilts you like, you will be able to decide what notions you need. For instance, I would not advise you to buy a bunch of tools used for applique unless you tried it and decided you loved it. Then I'd suggest you purchase a mini iron, some fusible web, a stiletto, and so forth.
When the instructions say to press seams in opposing directions, it means to press one block (or row) in one direction, and the next block (or row) in the opposite direction. The reason is because when you go to assemble the blocks, the seams will "nest" together and you will get perfect points.
I have a picture here somewhere that will illustrate this....
eta: okay, I found the picture. See how on the red piece I pressed the seam to the right, and on the blue piece I pressed the seam to the left? This will make the seam nest flat when it goes under the presser foot.
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Last edited by Peckish; 01-15-2012 at 10:12 PM.