1x Animal Courier
1x Observer Ward
1x Smoke of Deceit
2x Iron Branch
You would start the game by purchasing the Animal Courier, remember to activate this immediately so that you have space to continue buying the rest of your starting items.
The next item to buy is tangos (accidents happen, this will avoid using your ward inside the fountain).
Under normal circumstances you would only need to buy one ward but, you'll have leftover gold to buy the second one if need be. I keep one in the shop at all times for teammates who want to place them at a specific location.
Smoke of Deceit has a ten minute re spawn time making it important to buy one at the very start to maximize the amount of smokes you have during the game.
Tangos can be more useful than giving half of them to the mid lane player, use them on Iron Branches for an extended duration. This can easily bring you back to full health while waiting on clarity to expire.
Speaking of which, you'll be using your Freeze spell to lock down enemies that get too aggressive and for last hitting making these necessary until level eight.
1x Flying Courier
1x Observer Ward
1x Boots of Speed
1x Sentry Ward (2)
1x Magic Stick
1x Town Portal Scroll
1x Ring of Basilius
I place the Flying Courier in my quick buy as I'm running towards the hard lane's rune. 3:00 is a long time and at that time you might find yourself in the middle of a fight or stacking a camp.
One observer ward, and I mean it. You need gold for your items and as long as the the ward spot near your lane covered your mid player will have a safe place to go every couple of a minutes.
Sentry Ward or Magic Stick? If the enemy team has a lot of gang potential (Mirana Ult, CLinkz...) then buy sentry wards before buying magic stick. If getting ganked isn't a threat, then buy a Magic Stick first. This is great item to have because of how well it works against aggressive heroes like Bristleback.
Having a Bracer will give you the damage you need to last hit, alongside health. Buy a Null Talisman instead if you plan on buying Veil of Discord.
Keep a scroll on you; better to have it and not need it than to need it and not have it.
Ring of Basilius is optional. If you decided to max Crystal Nova over Arcane Aura then you may need this if you have mana problems.
1x Tranquil Boots
1x Magic Wand
Before going into details, Keep your core items short and to the point to give you time to think about what items are needed exactly.
Rylai will have a low health pool and slow movement speed until you farm enough gold for better items, use these in the meantime. I want to add that I'm against Power treads because
A) Attack Speed isn't important unless you're building to be a carry. The attack speed won't help much either if you're building for disabling.
B) Changing aura's to match your situation can be tedious and inaccurate without practicing. Not to mention if you switch to let's say agility to push down a tower (for example), your team may insult you.
C) Price, you really should be careful spending money, Crystal Maiden isn't cheap.
Last but not least, Magic Wand. This can save your life during and after a team fight.
Late Game Items
1x Gem of True Sight
1x Black King Bar
1x Aghanim's Scepter
1x Ocatarine Core
1x Shiva's Guard
Let's start by splitting this up into four categories.
Gem of True Sight is the definition of having a luxury
item, you won't need this against some lineups. this isn't core unless you're against heroes like techies or a fed Riki. Don't buy this if you're team is under farmed despite how much some people will cry for it.
Black King Bar and Aghanim's Scepter are your late game
items. Black King Bar prevents enemy spells from interrupting Freezing Field While Aghanim's improves the damage and slow effects. Pay attention to what the enemy team is building, if you notice there are items for Black King Bar then having one of your own may be preferable than buying Aghanim's Scepter first.
Late game items shouldn't be confused with Surplus Gold
Items (save for buyback before buying carry items). This is where point boosters come into play. You could save for either Octarine Core or Bloodstone. Buy Bloodstone first when both teams are pushing eachother in and trading kills. Buy Octarine Core when your team is winning those small team fights in the late game.
Here are the Author Notes from the in game item build.
Octarine Core: Surplus gold (Carry Item) Gives your spell damage life steal and provides stats.
Bloodstone: Surplus gold (Carry Item) Provides stats and a self deny, when activated; otherwise, heals nearby teammates upon death. The self deny also reduces re spawn time saving your buyback for later.
I include Shiva's Guard because it is a personal favorite item of mine. Overall, this is a good extension
item because it gives Rylai more damage and more slows.