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Hi, I've been playing some higher ELO games with Nunu. I always play him tank. I tend to start with a Health Crystal (and I have 3 quints of fortitude + 4 points in Veteran's Scar Mastery) this should put you almost 900 health to begin at level 1. (882 I believe) Even without the quints, you still have a load of health, and can accept early harassment. You want to keep on leveling, get that catalyst early, and then you are good to go.
With so much health, you can keep on hitting to proc your passive early game, and I recommend getting consume second, and keep on using it whenever you can(the CD goes down whenever as it levels up.) You pretty much should "ignore" the enemy unless they come up to you. Once you get the catalyst, feel free to spam on opponents (with a level 3 iceblast, hopefully.)
Obviously you might want to spam iceball early. If you do, then go sapphire. Knowing opponents helps a lot. IMO level 1-2 iceball are kinda a waste of mana, dealing not much damage, burning your mana. However, I have spammed before level 5 successfully too. Nunu is extremly versatile, and your playstyle should be adjusted according to your opponent. Sticking to a stiff guide will not help you in times you are ~200 health turret hugging, and you went for bloodboil instead of consume b/c a guide said so. On the other hand, if you are full health, have them running all the time due to ice blast, get blood boil then.