This is NOT the way to move from table-less layouts. You are still THINKING tables - rigid boxes each containing a piece to be positioned accurately like a jigsaw puzzle.
The whole point of current web practices is to emphasise CONTENT - first you have content, THEN you style that content to give the visual presentation you require. No content = nothing to style = no layout. This WILL involve thinking differently, where you will be positioning logically-grouped objects such that their relationship to other objects is determined similar to stacking blocks, and their positioning and/or size is allowed to move depending on browser resolution. Gone will be the days of slicing up a photoshop graphic and rigidly reassembling the pieces on the page - there is nothing wrong with laying out a design in Photoshop, just that you will use the individual objects rather than flattening and slicing the overall image.
So first think about the content of the site, then mock up an image of how you might want that content displayed, and then we can help further.