I noticed you mentioned Shyvana in your reply to Pure Panphobia. I would suggest going with her if you're interested in playing her and jungling. Currently she appears to be in a good spot, I've been seeing her played a lot recently and people are consistently doing well.
Shyvana is really strong as is Vi and Warwick, if you are into the bruiser types. But right now the domination rune and lethality are on top right now ( Kayn, Kha'Zix, Rengar etc...) if that is your gaming style. Otherwise, if you have played the support role previously its easier to transition into jungling with a tank type as mentioned in the other comments ( Rammus , Amumu, Zac).
What role were you playing before deciding to get into the jungle?
if you want to stick to the getting in your face champ, like braum and tresh then go for sejuani. if you want to try a different play style go for zac. I haven't played either champs but played against plenty. from my experience zac's early ganks are a much more threat than sejuani, since access to vision is low from the enemy support and you can gank from so many places as a zac. You should look at the guides and see if you like what they say about each and how to play them.
Domination is not at the top right now. The 3 highest performing junglers right now are Shyvana, Rammus, and Warwick. Domination rune is prevalent in lower ELO games because of massive snowball effects and being able to destroy the morale of lower ELO players, but if you want to play people who are the most solid, it's one of those 3 for sure.
Well, I am in the lower elo so I was speaking from my experience. Probably should have mentioned that. But lethality is really killing it right now that is for sure. Shyvanna and vi are dangerous at all times, but no one really picks them much in my games.
What role were you playing before deciding to get into the jungle?