Strength adds to Weapon Damage for EVERY class. However, if you are an Embermage, you are likely using Wands or a Staff. If you are using Wands or a Staff, then you gain Weapon Damage from increasing your Focus. The reason for this is that Focus increases Magic Damage, and if you look at a staff or a wand, you will notice that they don't do any physical damage - it's all elemental!
Now, there might be a couple reasons to increase your Strength as an Embermage - it WILL increase your Weapon Damage and Critical Damage, and may be useful to be able to equip certain gear. However, I find that the benefits of increasing Strength are minimal compared to the benefits of increasing Focus. Focus gives you a greater mana pool, allows you to equip higher-level Embermage-specific gear sooner, and ALSO increases your Weapon Damage by the same amount as increasing Strength! Therefore, I recommend increasing Focus as your most important attribute, with Vitality following, then Dex sprinkled in. (Usually for gear requirements.) I sometimes increase Strength if certain gear requires it and I don't want to wait until a higher level, but almost never otherwise.
Also, just a caution - Weapon Damage and Weapon DPS are NOT the same. Weapon DPS is a simplified display of a weapon's damage output, derived from a formula using Attack Speed, Weapon Damage, and more. Weapon Damage is the damage per hit of the weapon, as seen in your character stats screen.
The reason I mention this is because some class skills (I think Outlander skills, mostly) use Weapon Damage as a modified ("50% of Weapon Damage") and some use Weapon DPS ("50% of Weapon DPS"). So be sure to pick the weapons and skills that compliment each other best!
Another caution - some spells use Weapon DPS to calculate damage. Some do not, and are based on your character level and the level of the spell. (Hailstorm, for example.)
It sounds like the setup you've chosen will work just fine with a high-Focus character build, and feel free to choose the staff with the highest weapon DPS if you're looking to deal the most damage. And don't forget to have fun! :)