Veigar is by far one of the most powerful mage's in the fields of justice. If played right he can carry a team and solo towers late game. He is my AP main and I can pretty much destroy any champ with him( yes including tanks like galio). P.s. The cheat sheet does not show the true AP value in the build since it doesnt not factor in your Q farm which I get to atleast about +100 every 20 mins or so. It doesnt factor in passives such a rabdons and the elixirs.

For my runes I ideally build them for facing an AP mid. Standard runes would be
Flat Magic pen. Marks
Flat AP Quints
Flat AP Seals
Flat Magic Resist Glyphs

For the masteries I go for a standard AP offensive which would be a 21/9/0 or a 21/2/7

My first starting item would be a Dorans ring or boots and three health pots. I would then go back to buy a kage's lucky pick and rush Deathfire grasp. The recent downgrading of deathfire grasp was annoying since they took away mana regen from the equation made it more expensive and reduced the percentage of health taken away. Still a viable item for Veigar due to his unique skill of getting endless AP.

Boots- Sorc boots

Core items- Deathfire grasp, Rabdons Deathcap

Good items- Void staff or Abysal scepter depending on the situation.
Zhonya's hour glass helps with veigar since he is usually focused in team fights
Lich Bane is an amazing finishing item since by now you should have ideally over 1000 AP.( you can pretty much 2 shot towers with lich bane proc.)

The thing that sets Veigar apart from the rest of the Ap counterparts is that his power is limitless, it all depends on how well you farm his Q aka baleful strike. With this blessing you can destroy pretty much anyone.

Ignite is good on veigar if you put one mastery point in the mastery.
Clarity is viable since the death fire grasp lost its mana regen.
Teleport is good for going back for health and mana and coming back in to lane.(late game you can backdoor when you have full build since with lich bane proc you can 2 shot towers)
Flash is just an overall OP summoner spell good for chasing or getting away from sticky situations.

These are the most viable summoner spells for veigar.