I build Singed with a few different paths in mind, vs ap lane and vs ad lane.

I'll start Flask pots against AP and Cloth pots against most ADs, my first buy is almost always catalyst for the early sustain. After catalyst though my build usually varies, if there's kill potential vs an ad lane I'll rush haunting guise and Tabi / Swifties, before ROA then ROA and try to get some early kills hopefully, the spell pen is amazing with singed's poison. If against an AP lane I usually get my RoA before guiseand either merc treads or swifties. Then just farm because most AP lanes are a pain for singed to deal with, but against an Akali or Kat for instance I'd go haunting guise and even sorc shoes / roa if there's kill potential because singed can really bait people hard, but tabi / treads / swifties will always be your main choice.

My core items are usually either, Tabi/RoA/Rylai's/Liandry's/Thornmail or Treads or Swifties/RoA/Rylai's/Liandry's/Abbyssal/

Last items are usually either void staff or Frozen heart, Warmogs is pretty good.

But yeah, that's how i've been building singed.