The level system is borderline pointless, I think it is mostly there to keep brand new players from joining Ranked play with no experience whatsoever. There is an MMR (Match-making rating) you are issued, which rises and falls depending on who you win and lose against.
That aside, join PvP when you feel comfortable with a couple champions, and expect like 95% of your teammates to be jackasses. You may want to consider skimming across a couple champion guides on lolking (or some other LoL site) to get an idea of how to build items on specific champions. Also watching a livestream on twitch.tv or using the "Featured Game" spectator mode could help you get a grasp on how a typical PvP game will play out.
Welcome to LoL! Don't forget to ward and watch that minimap! :D
Edit: I believe the "Featured Game" mode is temporarily removed from the main screen, it will return eventually.