What size cutting mat should I buy?

18 by 24 inches is the most useful single mat, because it takes a folded width of quilting cotton. 24 by 36 lets you cut a full width without shifting the fabric, if you have the table for it. 12 by 18 suits small piecing and travel.

What does self-healing actually mean?

The surface closes behind the blade instead of holding the cut open. That keeps the mat flat, keeps later cuts straight, and keeps the blade sharper, because it is not riding in an old groove. Every mat here except the silicone pressing mat is self-healing.

How do I stop a cutting mat from warping?

Store it flat, never on its edge, and keep it out of a hot car and away from a radiator. Heat is what curls a mat, and once curled it does not come back. A warped mat lifts the ruler off the fabric and throws the cut off line.