I would just find lvl 70 gear and ditch your 60 gear cause they will be useless...
Typically attack speed is totally dependent on your build. Specific characters use it.
In terms of a character that utilizes attack speed, you generally use a witching hour, get base attack speed on your weapon and rings.
All characters:
The rule is critical hit dmg on your rings, amulet, gloves, and gem on your weapon. The max crit dmg you can get on your items (minus a weapon with base crit dmg or witching hour which is class dependent) is 330%. You want every bit of it.
The rule is critical hit chance on your rings, amulet, gloves, helm, bracer, and off hand. The max crit chance you can get off of items is 54%. Again, you want every bit of it.
Where you gain the majority of your damage however, is on gems that the greater rift guardian drops. The more you level your gems the more damage you are going to do.