Many makes the mistake, to play karthus for his ulti, i personally think his best weapon is the wall of pain.
Kathus is a fantastic long ranged mage, who has tremendes single target power, and unmatched crowd control.
The trick to play karthus with this build, is to have ice in your waynes, you will hold them of, or do dmg on range, and if they get close, you will prevale, a combi of high dmg and spell vamb, keeps you alive, and should they escape, you have the feared/hated ulti.
Never be afraid to go into batle or being jumped, because your wall of pain keeps the enemy slow and with no armor, and should you die, your passive will help you get at least one.
And remember, against single target in pasive, your q will do more dmg than ulti