Standard build is 0/30/0 with Attack Speed reds, MS Quints, Scaling Armor yellows and then Flat MR/Scaling MR/CDR blues depending on enemy team composition (usually scaling MR, but I'll use flat MR if the only source of AP damage is an enemy Elise or Evelynn for instance. I only use CDR vs full AD).
Frozen Heart is still really good situationally. You may lose out on some bonus HP from Ancient Golem, but since a lot of your effectiveness is from sustain through your Q, maximum health isn't as important as it is on some junglers.
Core build is usually: Machete/Pink Ward/Health Pot level 1, into Quill coat, into Sightstone, into Ancient Golem, into Boots. After that, resist/tanky items are best, usually starting with Frozen Heart or Locket. The only "offensive" items I usually build are Zeke's (15%~ of the time) or Abyssal (5% of the time) if my team composition is particularly imbalanced. Otherwise it's almost always FH, Randuin, Thornmail, Sunfire, BV, SV, etc.
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Do you ever lane with nunu? I've played him a few times this week in the top lane and have absolutely wrecking people. Not sure if it's dumb luck or he is just that strong. His sustain is unmatched and the harass from the snowballs is just lol.
Not very often, but it definitely still works. Another Nunu main named Simon hawkes hit Challenger about a week ago playing primarily lane Nunu. He held an AMA on reddit very recently- his build is approximately the same although he usually gets an early Hextech Revolver. I think that playing a champion that suits your playstyle greatly outweighs objective champion strength. Hell I saw a guy named Opened who mains Heal/Smite jungle Poppy who wrecked vasili with support Poppy.
A lot of meta picks are usually just copied from LCS, and people forget that the player pool in the LCS is quite small and that yeah- pros have their own favorite champions too- and that a lot of champions (like Lee Sin) are very high skill cap and much less effective in the hands of a Gold player than a champion like Sejunai would be.