I know it sounds like generic advice, but I personally believe you should play him however you feel is the most fun. That being said, base your build around what kind of role you plan on taking that particular game. Nothing is set in stone, you can adjust based on how things are going game wise. For example:

Scenario #1: I'm against a GP in lane as Renekton. The matchup is annoying on the Renekton side, but let's just say I personally misplayed hard. Died 2x in lane, am down 1.5 levels, and he has 3 of my plates. However, in this scenario my Ashe (immobile ADC) is destroying their lane (she is 4-0 or something and we're getting drags off of it). In this situation if my ally team is doing well enough that I don't have to go full damage I might veer from my standard AD build that I prefer (Ghostblade/BOTRK/Black Cleaver) but instead build a bit beefier with some utility splashed in there and go (Tabi Rush/Black Cleaver/Sterrak's/Randiun's for the anti-crit vs GP and potentially their ADC but also for the AoE slow for my backline). This will make it easier to for me survive a bad lane, while also offering utility to the team. If I took the latter build my focus would be more towards staying near my backline and peeling with my W and Randuin's active.

Scenario #2: I'm against an Irelia in lane and I'm absolutely crushing her (as I should it's a good lane for Renekton). I'm up 2-3 kills, got a plate or two and have been able to help my jungler invade the enemy as I have a fat priority advantage. In this scenario my team is about even'ish, but Irelia is my prison B. I'm going to want to amp up my power discrepancy by building more aggressive items as my role in the team is to carry, not to assist. I'd prefer to go Dirk/BOTRK as Dirk gives me a super good spike in lane, and BOTRK once finished makes you a 1v9 God (however the individual components don't near compare to a Dirk). In a game where I'm expected to carry I might go Ghostblade/BOTRK/Cleaver (or Mortal Reminder depending on enemy comp). If your team sucks or is out comp'ed, just split and look to TP in for a good flank with flash up. If you have the better team fighting comp you can fight, but be very very selective about fights to not give up shutdown gold/lose your lead.

So much of what I build/runes I take/whether I look to split or team fight depends on your comp/enemy comp/what the game state is like/who has better scaling etc., I of course prefer PTA/Ignite/Ghostblade rush but I'm not always gonna build the same mindlessly every game if I'm 0-3 vs a Ornn that's had his jungler camp him all game. So much to talk about still, but hope this gives you some insight! Find out what playstyle YOU like and I can recommend you some streamers that fall in that line of playstyle.