A hat is great practice, but if you're eager to get started on socks, do it! I also recommend using worsted weight yarn so that you can a) have more manageable needles, and b) see how the sock is put together section by section.
Also, I find it easier to manage the first few rows on dpns if I rest my knitting in my lap or on a table; that way the needles aren't flopping all over the place.
You can do it, Dina!!