Vulcan NEEDS movespeed, so always build charons coin or doom orb, depending on the enemy team comp. Pendulum is typically the best starter for vulcan, but conduit gem can be useful too if going for a Soul Reaver tank shred build. VS tanks I typically try to stack charons ASAP, then go into CD -> Soul Reaver, finishing with more pen like Tahuti. The main combo on Vulcan is to either 3->2->1 or 2->3->1.
Keep in mind that Vulcan's passive grants him MP5 and Movespeed, allowing him to get his full combo off even more easily if he has recently damaged an enemy with an ability.
For relics, I pretty much always start beads, unless aegis seems really potent. For the second relic, I typically go blink if the game is going well and I can play more aggressively, or aegis if I'm having trouble getting dove on. Phantom veil isn't a terrible choice either if vs an Odin or Cab.
Sands of Time
PASSIVE - This item grants 2 MP5 per 10% of your missing Mana
Spellbook
Pendulum of Ages
PASSIVE - This item grants 4 MP5 per 10% of your missing Mana. This item grants 7 Magical power per 10% of your available Mana.
Y10 Evolved Book of Thoth
PASSIVE - You gain Magical Power equal to 7% of your Mana from items.
Doom Orb
PASSIVE - Killing or assisting an enemy minion provides you with 1 stack, granting 1% Movement Speed and 4 Magical Power per stack. Stacks last for 15s and stack up to 5 times. Enemy gods provide 5 stacks.
Spear of Desolation
PASSIVE - If you receive a kill or assist on an Enemy God all of your non-ultimate cooldowns are reduced by 2 seconds and your ultimate cooldown is reduced by 6 seconds.
Book of the Dead
PASSIVE - If you drop below 40% Health, you gain a shield equal to 25% of your maximum Mana. This shield lasts 6s. This effect can only occur once every 90s.
Rod of Tahuti
PASSIVE - Basic Attacks and Abilities gain 15% additional Magical Power against targets below 60% Health.
Potion of Power
This consumable increases your Physical Power by 40, Magical Power by 70 and Penetration by 10 for 5 minutes or until you are killed.
Breastplate of Valor
Tyrannical Plate Helm
AURA - Ally lane minions within 70 units gain 25% Health and Attack Speed. Whenever an ally lane minion dies within 70 units of you, gain 5 power per stack, max 6 stacks for 15 seconds.
Backfire increases damage AND reduces cooldown when leveled, making it great for killing squishies and snowballing fast.
Your turret has built-in % penetration and can easily get multiple shots off against tanks, making it ideal to level when the team has a lot of tanks.
Vulcan does well against gods who are vulnerable during or after they ult. His meatball is great for stopping channeled abilities and popping nem's shield. His backfire helps gain a small distance which is crucial to escape kali autos after she goes on you. Similarly, it can be used to escape certain abilities like scylla crush or danza ult. His meatball is also useful to CC gods with stuns who are about to stun you, making them unable to attack you while you are most vulnerable.
People that can gap close on Vulcan even with the use of his backfire are deadly. Also anyone with a criple or long last silence can easily mean the death to a Vulcan. Gods like Ne Zha and Zeus can bounce projectiles off of Vulcan's turret, making his 2 very hard to use effectively. Also, gods who can becoome untargetable like Hou Yi in his leap or Janus in his portal can counter an incoming Vulcan ult. Jing Wei is a special counter to Vulcan, making his meatball bad to use on her, even for the damage (this is due to her ability to escape while mid-air).
Guardians with setup, especially AOE setup is great for Vulcan ult. Awilix can make use of her ultimate with Vulcan's ability to knockup opponents fairly easily. Khumba and Ne Zha ults are extremely easy setups, since the opponent is unable to dodge the vulcan ult, or even aegis it.