I started playing LoL a month ago and I second with Ashe. It's one of the cheapest champions and it's a very good choice for beginners.
Also, as Ten Inch Rooster said, I'd recommend someone with high difficulty. I started with Ashe and did pretty well, then I moved to Vladimir, which is not difficult to use according to the stats, but I found kinda confusing the health thing. And now I'm with Cassiopeia.
I also recommend, before PVP, go Co-op or create a Custom Game with your new champion. Just to get the hang of it (movements, skills, etc). I'm not saying you'll master it asap but everytime I saw a 'First time with [X]', I died a little.
And good luck!