If the concrete is all broken and moving around, you can't secure your deck to it. You haven't said whether your deck is going to be raised off the ground quite high (in which case, securing the foundations properly is critical) or as close to the ground as possible, but the other problem with cracked concrete is weed growth coming through, and that will carry on even when your deck's over the top. Its probably best to remove the concrete, but if its a concrete pad, it may be up to 9 inches thick, so depends what's there and how bad it is. If it is very thick and not moving around, its probably safe to put your foundation posts into it, but you'll need fence post type fixings with a flat plate so you can fix through to the concrete. Link here (its a UK one) giving general instructions re deck building, raised or otherwise, giving particular guidance on the foundation for the deck
http://www.diy-extra.co.uk/how-to-install-decking.html
As for what you put beneath it, a thicker geotextile membrane, the sort used under driveways rather than the common, thin 'weed membrane' sold everywhere. Spread it out, with a good overlap for joins of at least 8 inches, staple it down, rocks or gravel or whatever you can get over the top, doesn't need to be a deep layer, just something that will keep the membrane anchored down once the staples wear out, and to make it more attractive if the area beneath the deck is visible from another area of the garden.