A first project you might consider (rather than a scarf) is a neck warmer. I say this because scarves tend to get boring after a while, plus, to make one of any use, you have to knit and knit and knit and knit for a long, long time (which can be daunting as a first project).
A neck warmer, though, can still be a rectangle (and many are) and is much shorter than a scarf. You can also crochet button holes using single crochet and chain stitches along the bound off (or cast on--whichever you choose) edge.
You can check Ravelry for some simple neck warmer patterns. There are lots of them. They may require you to do the button holes differently, but you don't have to follow their directions. Instead, you can continue in pattern until the neck warmer is as long as you want and then do what I suggested above with the crochet!