Can I use just molding to hold down a floating floor or must I use quarter-round?
Most molding (skirting board) is 3/8" thick. You need a 1/4 inch gap around the floor to allow for expansion due to moisture.  So if you're going up right against the drywall, you'll have a problem with getting molding thick enough to cover it (minor variations in the gap WILL show).

One alternative is to buy the stuff they sell as window/door casing which is usually closer to 3/4" thick on one edge. This is a bit pricier, and can look a bit heavy.

An attractive alternative, which can give you a nice look is to use door stop instead of quarter round.  This is basically the same as using quarter round, but it's smaller and lighter, and doesn't encroach on the floor as much.



However, if your drywall doesn't come all the way down to the floor (usually a basement scenario) then as long as you have that quarter inch gap under the drywall free and clear, you should be ok with just ordinary skirting board.