The problem of suffering is one of the hardest things anyone grapples with, including believers.
I don't believe that there are neat answers, and I wouldn't trust anyone that offered them to me. The things people go through, the heart breaking things already mentioned on the thread, they are far too big and horrible for some pat and pious rubbish.
So, with that in mind, I'll answer as a believer. Suffering happens, and will happen whether or not there is a God. That's a pretty inescapable fact. On a purely practical level, there is less suffering among the people around me because I believe in God and this is part of my motivation to make the world better. So I choose to believe there is a God because that's the way I cope with the suffering.
I say choose, but belief is obviously a touch more complicated than that, and the reason I believe specifically Christian beliefs is because I also don't really feel happy with the idea of an absent God, looking on as we use our free will to destroy each other and the world. So I put a lot of store in the idea that Christians call 'the incarnation', which in untechnical language just means God becoming human, and being subject to suffering too.
Now, I know that's a pretty niche and weird idea, but it helps me enormously to feel that there is a God who understands what it means to suffer, suffers even now with those who suffer, and promises to end it at some point.
It's not going to satisfy everyone, and I'm not trying to convince - I offer these thoughts in the same spirit as the OP, as an explanation of why I believe as I do.