Hey while I'm 100% no expert Renekton, I've been widely successful of late with such scores as 11/0, 29/8, 17/0, 15/0, 13/0.. Etc. I'm crediting half of this to my prior experience with characters similar to Renekton and the other half to the shock value of this build.
It ends around with you sitting at about 3k health with 50% lifesteal and 450 damage. Which is beauty, you may not attack fast but with rage and your cull the meek and Dominus you stay alive alright.
And like my other builds this one is a maxim on surviving, what I find the greatest weapon in your arsenal, to be the god of death to minions as Renekton will directly translate to the enemy champions, don't be afraid but play defensively and you will dominate the lane.

DON'T BE FOOLED HE IS SQUISHY.

But illusion, is Renektons most powerful weapon.

You go with Cull the Meek early on, it's domination, poor minions still tell their children of the horror they witnessed at it's lifestealing sweep. If any survive that is.

First item you get, is the vampiric scepter for the sake that you're squishy early game, like unbelievably squishy, and if you can use Cull the Meek coupled with the scepter, fine chance you'll stay at close to full health if you don't commit.
Now I would not give any definite time in game or level where I leave the lane, it tends to be different every game, but I usually leave when I absolutely have to and at this point I buy the Ionian boots of lucidity with that cool down reduction and movement boost it is a cornerstone in your build.

Remember team work too it'll be your key to killing enemy champions, a lure then a slice out of the way, dice back in and stun while you get aid from a nearby gank. Don't waste the ulti too, it's free health.

Now the spells I've chosen are ghost and heal, why heal? Well more for a team contribution, and ghost to escape when exhausted or coupled with ghost blades active to make it impossible to escape you.

Renekton absolutely needs cooldown reduction, he relies on that, his spells are the only reason he's a feasibly good champion, that's why I've focused on life steal and damage for this build to maximise my stun and so I don't get killed off when silenced. He can pretty much solo any champion. So aim for your spells and you should be fine. He can also jungle well because of his lifesteal so think about that with this build.

Pro's:

1. Hard to kill and good damage

2. Movement speed isn't ever a problem, and you can easily get back to health while farming

3. Very cheap

4. Efficient killer and amazing mid game.

Con's:

1. If the game drags on a long time, you are at the risk of becoming easy to kill.

2. Team killing isn't so great but you can still contribute.

3. Attack speed is pretty weak.

4. Low armour and armour pierce makes alot of his attacks weaker then they should be.