Hello Lainey,
Yes, it s very safe to give them your social, they are a very reputable company.
You will be required to pay for a background check prior to being able to train, which is rather standard for the call center type business don't quote me but I beleive it was $45, unlike other companies they don't do a credit check, just criminal background.

The training, as far as that goes, the basic training to get you started is all free. And as new skills become available the will be offered to you free, for a short period of time, as well.. So all of the training I got was free. The one exception was I wanted an advanced training and I did pay for that, $15 but it was well worth it. Bottom line whenever you are offered a new training skill, grab it as soon as you can while it is free.

I have worked for a couple of the different call centers and of them ACD Direct was without doubt the best of them all.

Good luck