|This is a beginner's tip, or maybe just common sense, but since I keep falling into this trap myself, I thought it was worth bringing up.
Cotton and linen (100%) are wonderful fabrics to sew and to wear, but they need to be ironed. Moreover, they need to be ironed at high heat with lots of steam. That means that every part of your garment has to be able to "take the heat" - interfacings, trims, seam binding, any other fabrics you mix in.
Most interfacings, including all those nonwoven fusible Pellon-types, contain polyester or nylon. If you iron them on high, they'll melt and shrink and ruin your garment. Cotton fusible interfacing can be hard to find, but it does exist. Personally, I usually use a light cotton muslin, batiste or handkerchief linen and sew it in the old-fashioned way.
The same goes for trims. I just had a lace meltdown. Ribbons, piping - check the fiber content. Even silk and rayon could give you problems.
What if you don't know what's in an interfacing or trim? Use the burn test. Or, use Irene's non-scientific iron test. If you iron it on high, with steam, and it melts, feels sticky, or smells funny/oily, don't use it.
One more thing. Cotton and linen shrink, so don't forget to prewash interfacings and trims as well as the fabric.