Rek' Sai is a ganker Jungler, and is not the best in a lane. It can be done, but it isn't strong. She supplies 4 major things, good cc and damage in a gank, CONSTANT map pressure with her ult and good mobility with tunnels, and her burrowed form allows her to see people within the immediate fog of war
Downsides, in burrowed mode, you physically cannot see enemies. at all. EVERYTHING is the fog of war. And if an enemy is standing still, you can't see them burrowed, It's actually kinda funny. You in rek' Sai's jungle? Just clear her camps without moving, and when she isn't paying attention, move to the next one or just fight her.
Also, she is heavily gold reliant. The best thing to do is act like she is a juggernaut and go mostly tanky. (she isn't an actual juggernaut because of he rmobility but her mid game damage is strong enough-aka you build one-two damage items then go full tank.)
Her major power spikes occur at level 6, where you have insane map pressure and increased damage from the ult's passive. And after your first major item your damage increases drastically. She basically just scales after that by building tank and surviving fights.
Cinderhulk/Warrior are the best Jungle enchantments, as well as Chilling Smite. Trinity Force is a good item just for the stats and passives. Black Cleaver/Maw of Malmortius are great secondary items. But if you are just gonna go tanky I'd recommend titanic Hydra (regular Hydra if you need some sustain) Then just full tank ( I HEAVILY recommend Randuin's Omen)
All In all Rek'Sai is a very strong champion that takes a bit of skill to get down. Placing tunnels correctly is important, as well as managing them. She is insanely strong once you get used to her.
P.S. DONT BE DISCOURAGED BY THE FIRST CLEAR, I UNDERSTAND IT IS PROBABLY ONE OF THE WORST EARLY CLEAR IN THE GAME, BUT IT IS GREAT AFTERWORDS.