Imo, he's perfectly fine as is. Build him for burst and he is phenomenal, so don't waste your time on a Runnan's hurricane, that is a noob trap for AP Varus players. get a Lich bane instead every time, since it offers immense burst as the game goes on.
If you struggle with early game, here's a big tip: Max Q first. I know it sounds weird, but having high damage poke in the early lane phase is actually really impactful, and since you deal so much magic damage from your blight stacks because it is all percent based, they usually can't itemize against you effectively. You'll want to get Luden's first for some really insane poke damage on Q (at least, insane enough to catch people off guard), then rush Nashor's>Athene's>Lich bane>Rabadon's, finishing off with boots. Later on, you can trade your athene's for a void staff since your pattern changes from being about spell spam to AP DPS and only needing spells to proc your W.