Eh.. I wouldn't say that's a build I would ever use.
For my build here is what I would get from start to finish, it doesn't matter what order you build the items.
Longsword - HP pot
Longsword
Brutalizer
Berserker greaves
Bloodthirster
Starks Fervor
Infinity edge
Lich bane
That covers attack speed, cooldowns, attack damage, decent movement speed, good lifesteal, added critical damage, more damage when using decieve etc.
If wanted, can get sheen then turn it into lichbane right after you get your boots.