Do Buddhas think that suffering is bad or good?

Answer 1

To understand suffering you first have to understand why it arises. All things are neither good or bad, but just are. Suffering comes from our own selves attaching the idea that things should be different than they are for them to be good. So even though a head-ache is painful, the head-ache just is. We make it bad because we don't want it. So we struggle against it. That's where suffering comes from.

So, with that said, suffering can be overcome if one follows the Buddhas path (no struggle, etc). So no one, even Buddhists want to suffer, so we work hard to overcome it.