How about a half-granny triangle shawl? All you have to do is start a half-granny square:
Ch about 4, join in a ring, ch 3, 2 dc, ch 2, 3 dc in the ring, then turn;
on the next row, ch 3, 2 dc in the first dc, skip the next 2 dc, (3 dc, ch 2, 3 dc) in the corner ch-2 space, skip 2 dc, 3 dc in last dc;
next row: ch 3, 2 dc in first dc, skip 2 dc, 3 dc in space between first and second "clumps" of dc, (3 dc, ch 2, 3 dc) in ch-2 space...you get the idea. Keep going, varying colors or kinds of yarn or whatever, until it's as big as you like it. If you'd rather work it in sold dc so it doesn't have holes, or throw in some pattern as you learn it, why not? As long as you have the right number of stitches on the rows, or as long as you can get away with it, you can make a sampler shawl.