Solo Que Carry Top
Carried me to above rank 10. I'll add more later. With this build you deal substantial burst with the trait into your passive, destruction. The slow is great to keep people in range of your damage dealers while adding in some hurt of your own. The added shield stone skin is used when you engage. At 10 you should ALWAYS take army of dead it will get you through almost anything they can throw at you and ghouls often deal a good amount of damage if the enemy team is not focusing on you.
Army is always the better choice when solo queing. The only time the Shindragosa is good is when you have a full team you are communicating with. In solo your team has no idea what you're planning and often leads to confusion if you are using to disengage. Choosing the dragon also severely limits your tankiness and if you're the team tank, you've left the enemy a HUGE advantage in terms of survivability.
LEVEL 1 Top
Block is viable 99% of the time, if however you find yourself against fire and ice (jania and KT) or other mages that never auto, you might be better off taking regen globes.
Level 4 Top
Destruction 100% of the time, this is where all you're burst comes from.
The reduced mana cost of frozen tempest is tempting and i see alot of people picking it, but it does not add to you're damage that destruction brings. Once you are effective at turning you're aoe on and off Arthas has no mana problems anyway.
Level 13 the unmovable object. Top
Relentless, it is important to keep you're frost aoe slow on the enemies in order to catch them or peel for your carries. relentless clears up and control the enemy will throw at you as well as keep you moving to where you need to be. Arthas has low mobility as is, and passing this up will only hinder you in more ways than you can handle.
The frozen tempest triat is no good, as the damage from the ability comes from sustained ticks, so relentless helps you stay on the target the added 50% damage is no good if you are cc'd and can't be on them in the first place.
Trail of frost is no good, once you've played a few games and can land it, it's not important.
NOTE ON DEATH COIL Top
Literally 95% of the time you will cast this as a self heal, never mind the damage it is reduced heavily compared to how much it heals. If necessary you can use to secure a kill but don't bother if you're below 50% health, just be safe.
Burst i talk about Top
Hide in lane, root with your howling blast and walk in with frozen tempest to slow them. Hit them in the face with your passive and whala! You've dealt a huge damage burst and u can back out. IF they hit you a few times just heal up with death coil and wait for the howling blast to come off cool down.