I see too many people going with
which makes no sense for me
The jungle is very tough even for Rek' and
is much more forgiving and better in terms of farming, catching up, and speed. With Rek you want speed, she has the dmg mid-late game so no point in adding even more dmg which can be risky for the remainder of the gmae
She really works well with
because when she pops up from W, she can use Q 3 times in quick sucession thanks to her Ult. Normally, you can use all three within the time they are knocked up, then as soon as the third AA is done, you can use Hydra active and AA again, it's very quick and easy.
She works well with
because her abilities can be spammed in fight and out easily.
You don't need anything other than Jungle Item, Hydra, and TF. Rek has a lot of Base HP and as an assassin you don't need to get HP/armor/mr first. She needs 
As far as defense goes,
and 
With this build if you pop under an ADC or APC anytime during mid-late game, they either blow flash to save themselves or they die. Banshees is much better than spirit visage because the ability to stop one spell is much better than the extra HP or healing factor. Banshee's helps with assassinating much because most champs don't have 2 forms of CC. They need to stop you from popping up underneath them so it's hard in a 1v1 situation. IE, a Vayne split pushing can't kill you because at best she can tumble and dodge your pop up, she can't knock you back due to Banshee. Same goes with most APC.
Be careful of Cass thought, they can stun you will you moving towards them and they can blow your Banshee's easily. Kalista is easy as long as you can predict where she will hop next.
LEBLANC/Zed/FIZZ are the worst. They can kill you easily, faster, and dodge everything with extreme ease.