This guy have both damage and tanking ability, problems with him are in early game, when he is pretty squishy.
Core items for him are the archangel's staff and the frozen heart, 2 items wich work so great togheter, i don't think anyone need explanation, and force of nature, with it's much needed unique passive.
Considering the build of ap u make, sorcerer's shoes add much to your damage potential. They even offer advantage to those guys who favor thornmail or sunfire cape to other armors. Things change when facing a heavy cc enemy team, when mercury's treads are indispensable. What if you face a heavy ad team - tryndamere, master yi, miss fortune...? Don't get Ninja tabi, it'll ruin the use of your thornmail.
Well, talking about other items, my choice here for ap items would change for: rod of ages - more mana for ur archangel's passive, more life for ur force of nature passive, more ap, warmogs - i usualy don't buy it but i seen others do, great sinergy with force of nature but it's better for ad heroes like garen who may make good use of atma's impaler, Rylai's Crystal Scepter for his great unique, also a lil sinergy with force of nature, abysall scepter much needed against heavy ap teams, also decrease their ressitance which is good for ur skills, thornmail or sunfire cape.
I used before other more tanking builds, i find it cheaper to build chalice of harmony asap, like after you get the first item (regrowth pendant and lev 1 boots u get that item and then upgrade ur boots, this will make you a good farmer, even jungler, then get sunfire cape, force of nature, thornmail, rylai's scepter, then sell the chalice and replace it with rod of ages or with abysall scepter, but since i love ap amumu so much i prefer archangel's + frozen heart great combo.
Also, a great thing if u love mana to, if you go on defense mastery tree you get strength of spirit wich will help you regen hp faster, help you lane/jungle more.
Masteryes: i prefer 0/21/9, others may prefer 21/0/9 or 21/9/0, whatever is good for them (or they like).
Summoner spells: ignite work good with your despair and tantrum spells, also if you put the point in burning embers you get a lil ap while the spell is on cooldown. Ghost help you with chaising enemies, other good spells would be exhaust, flash, clarity, heal.
Hope you like my silly ideas. :)