Arthur is an in your face god who applies a lot of pressure to enemy gods, he has to be in order to build his energy up. Getting a point in all of your abilities is key right from the start then building your 1 fully first then the 3 followed by your ult and then the 2. I find this build to be the most efficient for me. Item wise building tanky is a good start if you are still learning him, as you gain more experience you can start building more bruiser.
CDR is always nice on Arthur but isn't a must for him. Overall its your play style so find what works for you. I tend to be super aggressive myself.
As far as items go I am not going to talk about starter items or anything like that. Just each item that you could build and why you might want to build it.
This item is a must. The passive it provides by healing 2.5 percent of health and mana is key in team fights. It procs on every of his abilities but not only that it also procs on every god that is hit. So it stacks per god. So if you hit 3 gods with one ability. that is 7.5 percent of health and mana that you get back. It has saved me in team fights more than I can count.
As far as boots go this is prolly the better option for the power boost. Straight forward really movement speed power and sold for a different item late on.
If the Solo laner is physical I almost always go void shield for the extra damage and defenses. The passive works well to weaken the enemy gods defenses as well. This allows for more pressure in lane.
So when you are facing a magical solo this is the item I usually go for my initial magic defense. It provides defenses health and cool-down reduction so you are able to combo abilities more often which is always good for Arthur. The passive takes time off your cooldowns if you are hit by a magical ability. I almost always have this item in my builds cause it is a good magical defense item as well as on being on the cheaper side.
Some people ask why blackthorn hammer. Well for me its mainly for the health which as you know from glad shield the more health the more you heal up. It's passive is nice allowing Arthur to stay in lane longer because of the mana sustain when mana is low.
The obvious reason why you would build pestilence is for the anti heal which reduces healing done by gods in range. The health boost is also a nice plus.
To often I find myself being straight shredded by hunter and auto attack gods. This items make them do half their normal crit damage which can save your life if you are trying to fight or get away. Also since CC is crippling to Arthur the CC reduction helps with that.
This item is good for keeping the auto attack gods off your back, not much to it really just reduced their movement speed and attack speed. The health is nice however for glad shield procs.
Hide of the Nemean Lion
This item is to help counter auto attack gods as well by reflecting 25 percent of auto attack damage.
Why soul eater. well when its built your abilities heal you for 15 percent of the damage dealt. Great way to heal off minion waves and combine with glad shield in team fights makes you difficult to kill. Cooldown and extra power are also beneficial.
I get crusher on occasion if I want more power. The pen is nice but the attack speed does nothing really. As for the passive it procs on every ability and damages an enemy god for 20 physical plus 15 percent of your power. It can add up over time. If I do buy this items its usually after boots are sold.
Brawler's Beat Stick
This item you would build to counter healing as it procs on abilities which Arthur has 8 of. So its a nice replacement for crusher if need be or if your team needs anti heals. If I do buy this items its usually after boots are sold.
Gauntlet of Thebes
Gauntlet of Thebes is one of my favorite items if not my most favorite defense item. With the buff it now gives you even more health but isn't really useful in the lane phase as you need passive stacks. it provides hp5 275 health and 50 physical and magical defense once stacked as well as an aura for your teammates. It is a nice item for late game but difficult to get stacked in the solo lane. If I do buy this items its usually after boots are sold.
Runeforged hammer gives you power health and a nice passive that procs on 2 of Arthur's abilities. The 15 percent extra damage on cc targets can go a long way however if I do buy this items its usually after boots are sold.
This item is a good overall Item for Arthur is provides defense for both physical and magical. It also provides cooldown and cc reduction which goes a long way on Arthur. Its passive provides damage mitigation when hit by hard CC which can save your life. If I do buy this items its usually after boots are sold.
Mantle of Discord
Mantle is usually my last or second to last Item built most of the time after blackthorn hammer lately. The defense it provides is great. It adds to the cooldown redcution and if you take damage below 30 percent it stuns enemy gods around you for one second and makes you cc immune. This passive can be devastating in a fight especially since you can then land you abilities and heal from glad shield allowing you to comeback on the opponent/opponents. A must have in my opinion.
Hope this helps you understand why I build some of these items in my builds.
In games where I am building more damage I will usually by a 3k defense pot to boost my defenses. It helps a ton.
In my opinion the must haves on Arthur are
Mantle of Discord