First Item:
For survival, if the enemy team is heavy engage or assassin, or if your team lacks engage and may likely need you to engage/peel.
Damage.
If you're in a poke comp. It does more damage, but GLP will usually be Superior for damage unless you're in a poke comp.
You're not really mana hungry enough to need Athenes, and you don't really scale hard enough to justify the Late game build.
Second item:
Still the best damage item on Morg, and Oh my God, so much better then before. The changes suit her perfectly! Damage amp to multiply her already high base damages, occuring over time works really well with her "dot"-like kit.
This item is pretty much synonymous with Morg. "Afraid of engage, need to engage" or just laning vs Zed.
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Vs Le'Bitch. Keeping the bitch from getting fed is the only thing you can do to impact any Le'Bitch matchup. Spirit Visage is a little extreme, and if you do ever feel like you need it, I'd recommend stopping at Cowl, building Haunting Guise, and then finishing SV and then Liandry.
Vs extreme Healing. You can point and click apply GW to multiple people from range with pool.
If you built damage before and suddenly regret doing so, Rylais is the best choice you have to back out of the damage build.
If you built RoA first but feel like you need more CDR now, GLP, Zhonya, or Banshee's are your best options.
: Only if you're on a poke comp, even then Liandries is probably better.
Third item:
Is Void Staff. It is the third item in every build. only really put off if the enemy team has no tank and you're snowballing so hard it doesn't matter what you build. The only item you would ever really consider putting this off for is Zhonyas, or I guess Liandries if you're vs Zed and already bought Zhonyas.
Fourth item:
Past this, you'll usually be picking more of the previous items, but Rylais, Liandries, and Zhonyas deserve special mentions.
Runes:
Sorc will usually be your main.
Comet
Ultimate Hat/mana band, depending on how your opponents resource is. Mana vs Zed is the only obvious one off the top of my head.
Transcence if you're building RoA or want 30-40% CDR, Celerity for Poke comp.
Last tier is a toss up, scorch vs Gathering Storm is almost personal opinion and the best choice will change from match to match, waterwalking if you want to Gank. Morg Ganks are pretty good.
Damage builds should pick Domination as their second Tree
Ravenous Hunter is a Must.
Your other choice is Cheap shot for more damage, or Taste for blood.
Defensive builds should take Precision second tree, Triumph can heal you for a LOT if your team picks up a kill while you're in Zhonyas.
And obviously the mastery that does more damage against low health enemies. I forget what it's called... >.>
TL;DR example builds:
Defensive:
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Offensive:
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Poke:
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For top lane, most of the above still applies, but with only a few adjustments. Top lane Mages should lean more towards defensive and utility builds, because their teams should have enough damage and by taking a mage top, you've removed some safety from your team. This isn't a terrible thing though, because a lot of mage tops have enough peel to make up for it.
Biggest difference is that you'll prioritize catalyst first, and you can optionally put of completing your catalyst and instead build
latter in the game.
Also, Void staff is a lot more optional on top lane mages, especially ones that build Laindrys and can add decent tank damage on top of the rest of their teams damage. Use this to your advantage by building combinations of Liandrys, Zhonyas, and Rylais. But still build Void staff 4th item.
Unless you're on a poke team. THen just build the poke Team build.
In the jungle, just ignore Catalyst, it's not a viable jungle item. Just treat
as if it was Ludens, and proceed accordingly.