If you can build a Turbo Miata, you can tune up a bike. That being said, even the most mechanically-inclined ppl cannot make a "BSO" into a proper bike. Not on a tight budget, anyway. Which is why I suggest looking for the older, trickle down tech-equipped x-mart bikes. I don't doubt that, with a little bit of love (and a little less paint on the rims), the "Schwinn" from the original post can be made into a reliable, serviceable bike. But, I'd be wary of any x-mart discs in the year 2014, as they're likely to be pretty bad examples of a disc brake. That will likely change in the future, but I don't think BSO discs are "there" yet.
So, hopefully, removing that paint will do you fine. As you've already surmised, the current pads might be contaminated, so you might want to be ready to get ne pads, too. It'll be cheaper to go that route, either way, and I feel 98% certain that the painted braking surface is he cause of your woes here.