I'd Always build tear on Karthus, He needs the mana for his defile. You can skip out on RoA as both tear and RoA might be too slow. Haunting Guise + Sorc boots depending on how you see the game going can grab you some early cheesy kills because your ult will effectively do true damage to your targets early game when everyone is building core damage items. Build depends largely on style of play. Are you looking to grab cheesy kills around the map while constantly shoving in mid not giving your opponent time to roam and threatening first tower if they do? Then I'd just go full pen early (sorc + haunting guise for true damage) get a rylais, upgrade the haunting guise after rylais for synergy and build any other AP items i feel necessary after that, (Void, zhonyas, deathcap) Taking TP as my summoner so i can always push mid. Are you looking to scale and duel it out in lane? well RoA is better for that and taking exhaust is best summoner in that case.
Rylais abyssal and zhonyas is too defensive a build. You have to remove one of them depending on the enemy team's damage type and add either Deathcap or Void depending on their build. (a lot of MR void, a lot of health - liandry's - not much defensive items - deathcap)