You're squishier than other classes, and so you need more life and armour buffers to avoid falling foul of any poorly-picked fights.

Levelling a Wizard isn't necessarily any more challenging than levelling the other classes in Softcore mode, but in Hardcore - where death is permanent - you need to be much more on your toes. Diablo 3: Xbox One X vs PS4 Pro 4K Dynamic Res Graphics Comparison!

If you've unlocked the Mystic, you'll be able to get those slots rolled in, otherwise you'll have to get lucky with your drops. As you level up, try to socket a good Ruby into your weapon for the damage boost, and another one in your Head slot for a minor buff to your experience gains. The Wizard's primary stat is Intelligence, and so all of the items you equip should be positively dripping in this damage-buffing stat. When you've tired of dropping fiery meteors on your enemy's head, perhaps you'd prefer to transform in a spectral disco machine, firing laser beams out of your face. It takes in all of the magical schools you'd expect for the character archetype - fire, ice and lightning - yet there are less traditional avenues to explore too. It's somewhat vulnerable, yet its damage output is vicious. Diablo 3's Wizard is about as satisfying a glass-cannon character as you could hope for in an RPG.

Diablo 3 wizard skills guide