I don't know that newspaper will have much affect on the weeds, but it wouldn't hurt to try it. I would try to kill the weeds with an herbacide (such as Round-Up) first, and apply enough wood chips to make a new layer a few inches thick. The depth of the woodchips is usually enough to smother any weeds, and future weeding is usually quite easy when plants root in woodchips instead of soil.
I would do it this autumn, rather than waiting until spring.

if you're intending it as a playground- I'd avoid the herbicides.

just on principal, even if you don't believe the arguement that such things aren't as biodegradeable as they claim.

in general- rake away the existing mulch (you'll get some of the weeds as well) put down 3-5 page deep layer of newspaper, wet with hose, repeat until you have 10-12 sheets down everywhere, wet with hose one last time, and then bury it in 3" of fresh mulch...I prefer the ground mulch to the wood chips, but that's a matter of personal preference.

I'm slowly reclaiming a yard left fallow for a decade with this method, and it's working better than any other method I've tried.