The meat and potatoes of the guide. Renektons item build can change drastically from game to game, and once you get some experience with him, you'll be able to make your own judgement calls. For now, you can refer to the item in question and see what I think of it here.
Doran's items are awesome. They give you great early game stats, and the damage block on Doran's Shield specifically is fantastic against autoattackers. It's not uncommon for a good Renekton build to have at least 1 or 2 Doran's items to help you reach your other, more important purchases. They do have their downsides, however. In the end, they do they delay your more core items, and they start to become a bit of a gold sink if you buy too many.
Black Cleaver is probably Renekton's single best item - you can once again build phage in the early laning phase, which arguably has the best distribution of offensive/defensive stats in the game. An early Cleaver upgrade will give you additional HP as well as a bit of CDR, all of which you want at some point in the game. Brutalizer is very comparable in terms of power to a Phage, but Ghostblade is much worse than a Black Cleaver as the game goes on.
While Frozen Mallet is good on Renekton, I would say it's just a tad expensive for the stats it gives you. You should be looking at the other Giants Belt items instead unless you absolutely need the guaranteed slow. At the end of the day, Frozen Mallet is a utility item that fits into a very niche role.
A great item on Renekton but not quite core anymore. The magic damage helps you win trades in lane and overall it's a really nice mix of offense and defense in one item slot.
Decent in very specific situations. If you know for a fact the enemy ADC isn't going BorK and the enemy team has an even mix of physical and magical damage, Warmogs is a decent buy.
Probably the best all-around armor item in the game. Armor and HP in one item slot is ridiculously good. The active allows you to peel or stay on top of a target. Its hard to justify not getting this item almost every game, as its just so good in so many situations.
Might be the best straight up defensive MR item in the game.
Thornmail is totally underrated, and in my opinion it's actually the best late game
Armor item. Essentially, it cancels out the enemy ADC's lifesteal, and during late game teamfights this is huge. If you're able to reach the ADC, it's almost impossible for them to not take damage in some way.
If you're a high priority target, or you need to dive into the back line to fight a carry, this is a good route to take. GA is also gamechanging in the late game when respawn timers are so long or the next fight will determine who wins and who loses.
This is an essential pickup if the enemy team is stacking armor and your team needs you to be an extra source of damage.
Really powerful in certain lane match-ups. Great against champions who rely on magical burst damage to win all-ins.
Right behind Banshee's in terms of MR items. The CDR and HP are great. If there were 2 routes, one leading to Banshees and the other leading to Spirit Visage, I would consider SV to be the more offensive of the two.
Gives you a very small amount of sustain and more importantly, a bit of extra sticking power.
I think Ravenous Hydra is the best DPS item you can get on Renekton. It allows you to push waves instantly once you group them up, it gives you more AoE damage, the health regen is good in lane, and it can cancel your W animation. You can also just sit on the Tiamat without going the distance to upgrade it, which is nice considering you can use the 1400g required to buy Hydra and put it towards tank items.
Mediocre damage item. Hydra definitely more useful in most scenarios, but the lifesteal from BT is much better.
Bad item Renekton. Attackspeed is one of the least beneficial items on him and Wit's End doesn't have the best synergy with Renekton as a champion.
Ok guys, let me rant a little bit about Trinity Force. I will admit, it's an ok item on Renekton. The sheen procs, the HP, the movespeed, the chasing ability - all the stats, minus the mana, are useable in some form or another. But if mid-game rolls around and all you have to show for it are some dorans blades and a TriForce, then your team is going to get rolled in skirmishes. The items I suggested are much better at fulfilling the role your team needs mid game. TriForce is cool, but you just dropped 4K gold for something that offers very little survivability in terms of HP and resistances. Just because Dominus gives you bonus HP doesn't mean you can build something as purely offensive as Trinity Force is. At the end of the day, Trinity is a luxury item.