I find that most games that I watch with my Diamond friends, here's the list of the most common ones :
Vi, Shy, Lee, Ww, Kha, Xin, FIddles, J4.
Pretty much anyone with a high clear time and either sustain or a shield. (or both, in Lee's case). Shy being the exception, her w being so rapid with clear right now that she doesn't much need sustain after level 5. (3 points in w melts camps).
Of those, I find Vi or WW good starting junglers. They both have can't miss ults, and great gap closers. FIddles is easy to clear with, but super hard to gank with if the opponent is warded, due to the lack of a real gap closer save for a charging ult that most people will run from. He's unreliable as you get higher up in ranks, as more people ward.
Honestly, I've had the most reliable games with vi. She hits like a rock, and has a lot of disruption to either split the opposing team or peel for your carry.
If you want additional assistance jungling beyond that, the Diamond friends I mentioned earlier do free coaching :
http://boards.na.leagueoflegends.com/en/c/tips-tricks/W7KqoJiI-free-coaching-from-diamonds
Feel free to swing by. =)
-T