A scarf is the most common first project. A felted purse or lap-top sleeve is another great first project. If you've knit your scarf in feltable yarn (see below), you may even be able to stop half way, and seam it into a purse and felt it. A hat on circular needles is another fine project. Whatever you choose, be prepared to embrace the quirky imperfections that go with the territory of any first project. If you'd prefer to hide imperfections, felting works great. Felting obscures details that smooth yarn would otherwise show readily.
Warning: If you make a scarf in the lovely stockinette stitch (alternating a knit row with a purl row), the side edges will curl in. You will have a rolled-up tube of a scarf! So I don't recommend stockinette stitch for a scarf. Use garter stitch instead (this is all knit stitches, back and forth for every row, or some other pattern or alternate knit and purl stitches.
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