The best option for strong AD lanes such as Riven, Renekton, Lee Sin.
This start is good against ranged harass such as Jayce, Kennen, Nidalee. If you don't feel safe starting with only one potion you could opt for a different start and get this item on your first back instead.
The best start against pokey, AP champions if the enemy team has a strong early game jungler with ganking presence (Ex: Lee Sin, Jarvan, Mirror Zac, Maokai, etc)
The best start for pokey, AP champions if the enemy team has a weak jungler (Malphite, Amumu, shyvanna, etc) You'll probably end up selling one of the beads unless you can make both Bulwark and Locket for your team or you opt into warmogs (not recommended) but that's perfectly acceptable.
This is pretty much the only damage item you will need to burst out squishy laners. Zac scales better with magic penetration than AP so Haunting Guise is the perfect offensive option for him. Usually you will hold off on the upgrade to Liandry's until very late in the game. You can consider skipping this item if you are against a top laner that you know you won't be able to kill and opt for more tankiness instead.
Sunfire cape will give you more sustained damage and pushing power. Since you already deal AP damage the magic damage from sunfire will go well with your magic pen. Sunfire is a great item for midgame fights and will give you a lot of survivability against AD threats.
Items to Consider:
Good against and in double AP comps, this item has no health so you'll probably want to build a giant's belt first though. If someone else on your team can build this it would probably be best but it isn't a bad pick up for Zac.
If your support or jungler doesn't have this yet you can buy this to help against AOE damage and to protect your team. The CDR is also great on Zac and the shield can be spammed in lane to win trades.
This item is good against attack speed based bruisers and AD carries and increases your initiation potential with the slow. Buy this if the enemy ADC is a large threat or if the enemy team has Blade of the Ruined King. A well placed Randuin's active can cripple the enemy team and turn a fight around.
If no one else on your team has this item buy it, especially against heavy AP teams. Team auras can make or break team fights. This is the best MR option besides Spirit Visage for Zac.
This item is very popular but rather mediocre in my opinion. It costs a lot of money for not many stats. You already have a slow on your Q, a knock up on your E, and a knock up on your R. Your abilities are all AOE as well so you won't get a full slow. If you really feel like you need more CC Randuins is probably a better option.
Spirit Visage's passive is very powerful in conjunction with Zac's Blobs and gives him a lot of sustain. The CDR is also amazing on Zac. This is one of the best items for Zac so if the enemy team has enough AP to justify this purchase then get it. Buy this against AP top laners or heavy AP team comps if your team doesn't need a bulwark/abyssal scepter.
If the enemy team has a lot of AD auto attacking threat or if the enemy AD carry is extremely fed thornmail is the best source of cheap armor. Synergizes with your magic damage and magic penetration and the effective HP you gain from your passive makes this buy more worthwhile for Zac as opposed to other tanks.
I don't recommend warmog's because it is HP overkill. Stacking too much health without resists makes you vulnerable to percentage damage and you need to properly balance your health and resists to get maximum effective health. There is no point in having a large health pool if every attack from the enemy team chunks you.
A solid defensive/offensive option. I usually buy Zhonya's when I feel that I am tanky enough and want to do more damage or as my 6th item. The active can save your life from very readable spells (Death mark, requiem, crowstorm, etc) and gives you even more diving potential in conjunction with your passive. As a bonus, Zac has a lot of fun poses to Zhonya's with.
-Note that if you zhonya's during Zac's ultimate you won't get any more bounces when zhonya's ends.
I really don't recommend getting GA on tanks but sometimes in order to win the final late game team fight it's what you need. Also having double revive passive allows you to make a lot of aggressive plays.
A good increase to your damage. If the enemy team has multiple AP and not a lot of CC this is a good option.
The best defensive boot options, get these against heavy AD teams or fed AD carries or if you want to prioritize tanking over dealing damage.
If you need MR/Tenacity get mercury treads. Never pick mercury treads for just one or the other, it isn't worth the money.
Buy/Upgrade your boots when you plan on roaming/initiating, in lane boots aren't very useful since you have a long jump to escape ganks.
Don't forget to buy consumables when you back. Consumables can make or break lanes and are solid investments.
Just because Zac has a lot of sustain doesn't mean health pots aren't good. If you get too low and are zoned away from minions your passive won't be able to heal you up and health pots can help you survive close fights and ganks. If you are getting ganked or going in for a fight always remember to pop a health pot, it could save your life and even net you a kill.
Wards are very important for being able to play aggressively and controlling your lane. Always buy at least one ward unless your jungler loves you and wards for you. Even after laning phase try to pick up wards if you can to help your support keep control of the map.
Pink wards are very important for Zac to get a proper initiation in mid to late game. Even during lane phase you can set up ganks for your jungler by denying vision from the enemy top laner. I'll mention this several times throughout the guide, Zac top in conjunction with jungle ganks is deadly and unfun to play against.
Remember to pick up elixirs before important team fights such as baron contests, sieges, and late game fights that could determine the game. Fortitude elixir will make you tankier and brilliance will allow you to do more damage and spam more abilities to heal.
Late game you could buy oracle's for your team if your support/jungler don't. You're probably the tankiest person on your team so it's safest for you to clear wards.