i'd leave the old stuff there, if there is any chance weeds/grass migh grow throuhg lay your newspaper/cardboard over it before adding anything else.

not into using peat, so source some good recycle composted material or any composted material, our prefference is for mushroom compost from the farm. not sure what sort of garden it is going to be but if it is for vege's then i'd suggest using a spoilt hay type mulch instead of chipped wood.

take a look at the pic's on our site there may be some ideas there for you?

len

Here is a link that might be useful: len's garden page

The compost, leaves, and pine needles are all materials that become Peat Moss except htose materials have the nutrients that will feed your plants while the Peat Moss has none. Aside from being a large waste of your money to use Peat Moss is a non renewable resource and need not be used unless you have no other source of organic matter for your soil.
Just plunk your new mulch material down over the old which is on its way to feeding the soil under that mulch. Removing the old mulch will stop the soil feeding process until your new mulch has been digested enough by the Soil food Web to be of some value.