If a champion on free rotation looks even a bit interesting to you, try them out. Playing a lot of champions is a very good way to learn about both those champions and your own playstyle.
Make sure you're playing those champions in more or less the right position, of course (Ranged AD bot, Support bot, Mage/Assassin mid, Honestly just do whatever the fuck for top/jungle you'll start to figure out pretty quickly what is and isn't suicide in those positions). Doing something silly like Sona jungle, as an extreme example, can ruin your first impression of a champion. Though, again, top and jungle don't have rules as easy to understand and mid and bot.
Don't even touch jungle without a full rune page, unless you're using Warwick or Nunu (both of which are valuable gameplay experiences for a new player, but not really that great once you start to git gud). Also don't forget smite.
Don't get discouraged by failures or flamers. I'm in plat and people still don't know what the fuck they're doing. Including myself. Play so long as you're enjoying yourself, and take a break when you're not.
I don't have the sort of free time that lets me promise to play with you, but you have my best wishes with you out on the Rift! If mid lane's your game, I'm a bit more knowledgeable there than some others, so feel free to throw some more specific questions about mid lane and mages my way if you have them!