League of Legends (LoL) Question: Veigar starting items

Definitely take Doran's Ring if you take Teleport. You could consider Crystalline Flask in matchups where you are 100% going to take harass early. In general it's better if you can get away with ring.

Think of it this way. Will Flask sustain get you 15 more lasthits with your Q? Probably not. Doran's ring is much more efficient UNLESS you get forced out of lane due to lower health sustain (losing XP and gold). Then Flask is more worthwhile.

If you take TP (some Veigar players do) then you can use TP to "sustain" in lane early so go Ring all the time.

Doran's Ring is a viable item if you are considering to be a late game monster with your Q, although it is always viable to farm anyway with your Q.

If you may suffer from a harrass lane or are matched up with very mobile laners like Zed, Crystalline Flask or Boots of Speed with 3 Mana Potions and 2 Health Potions are always ok.

You could also go for the risky Tear of the Goddess rush by taking a Mana Crystal and 2 Health Potions however you should only do this if you have Teleport and if you do plan to go for Tear of the Goddess First, you are hurting Veigar's Early game and compensating for his late game with the Tear Stacks.

I always take the ring, because of his passive. Even once I've used all my mana, it doesn't take long to get enough for another Q. The way i do it is once you get a point in E, keep 100 mana in your pool for ganks, just in case. When I have 160 (one point in Q, 170 w/ 2 points) then I'll use Q. As long as your opponent isnt super aggro, and you can dodge skillshots, you should be able to stay in lane for a while, stack Q and get enough for a Tear for extra mana.