galio main here
option 1.
->
->
->
->
->
/
(choose one then build the other) -> fill
i reserve option 1 for general assassins or i despretley need the HP in the long run to survive poke/burst.
option 2.
->
->
->
-> fill AP build here, any ap items work really, just take your pick.
from abyssal i generally go
->
->
-> 
option 2 is my bread and butter for most matchups where you need a galio to deal damage and carry a team, this will full combo a ADC without a banshees/GA and assuming i land Q=E while getting a max ult off.
i've been dabbling with
its ok, but i find myself reliant on the active damage and it lacks cdr so i typically need other items first.
galio was hurt with the grail change, but with the ap itemization update it became managable again, assuming you take mana regen runes/meditation and maybe add in a little scaling cdr if you want too, but i prefer penetration/magic resistance for early game dominance, galio will hit hard and have a really good amount of bulk, the only issue is early game last hitting, if you can do it you're a god.
galios Q easily deals more damage than any other poke ability, even viktors laser. so they will eventually have to back assuming you TRADE and you aren't take FREE POKE while you fail to last hit minions. W will heal you back up and you will outlast your opponent.
galio cant SPAM like he used to with grail, but if you just hit your 2 skill shots and heal yourself galio is really really good. you flash ult at 6 and its a free kill for you or your jungler every time.