seems to fit you're requirements. She's also very straight forward and easy to play.
Her binary play-style makes her popularity go down the further your elo goes up (we all know what she's going to do and how).
But she has innate tank, good AoE, jungles well (counter-jungles really well, ganks not so much), and mixed damage makes her hard to build against until mid/late game. Decent mobility in the form of a huge speed buff and super long range dash on ult (that can be interrupted by butterflies), and a small knock-back on her ult as her "1 cc".
She can also top and mid in a lot of match-ups (pray you don't face a heimer).
That out of the way, I would recommend just keep going with the free week champs until you find someone you really like / click with. Otherwise you might end up like I did with Fiddlesticks.
He was recommended by a friend who knew that my play-style in most games is annoy the hell out of opponents (Infinite damage reduction deck in MtG, anyone?). Unfortunately, even the cannon minions call it a "free kill" when I play him (don't get me started on elder lizard).