My off-the-top-of-my-head recommendations for ToJ members new to LoL:
Don't play with strangers while learning. The LoL community is one of THE most toxic gaming communities online. I enjoy learning new characters when playing with ToJ members, but I wouldn't even attempt the same with random LoL players.
You shouldn't have any trouble finding other ToJ members to help you learn the game, so fret not! If it's all for the purpose of instruction, I'd even be willing to play LoL more than once every two weeks.
Don't play as Ashe or other super-squishy characters while learning. It's just frustrating. I almost quit the game after getting stomped multiple times in a row. It wasn't until I found a sturdier character that could still do reasonable damage that I started to enjoy LoL.
A character like Sivir is fantastic for a new LoL player. Nunu would probably be a good pick, too, depending on your play style.
In fact, I'd recommend telling us about your play style preferences and we could probably recommend a few good characters to try based on the information you post.
On a related note: Pay attention to the "Difficulty" rating of characters in their profiles. I strongly recommend playing any champs listed as "Hard" Difficulty for a while. (I seriously don't know why Morgana is listed as "Hard" Difficulty, though.)
Try not to buy a character until you've played as him or her. You can check
this link (which I suggest you bookmark) to see which 10 champions are free to play each week. The free set tends to include a good spread of character types and will help you learn which and what types of characters you enjoy playing as.
Get on the CGA TeamSpeak Server and join one of the ToJ LoL chapter channels when you play. Keep
this server status link handy, too.
Ask questions! The LoL community at large may be toxic, but the ToJ LoL players have been wonderfully patient with me. I would have uninstalled the game after the tutorial if not for Mostly_Harmless taking the time to help me learn the game.
Those are just some starter tips, but I hope they help!