Although cardboard does eventially break down, it may take more than a year. The thickness can block moisture in the soil, so any alliums may suffer. The shreaded leaves and straw are better choices, as they allow water to flow through and evaporate easier. A few layers of newspaper might be a better option. If you want to really clean up the bed, a cover of clear plastic all through this summer (if we ever really have one!), can act along with the sun to sterilize the soil and reduce any insect or pathogen problems.

One layer of corrugated cardboard under straw will disintigrate in no time, especially if kept moist.

Two months ago, I decided to get rid of my lawn. I covered the grass with 2 - 3 layers of cardboards or several layers of newspapers, watered them down, then spread a couple inches of mulch over the papers. As I accumulate more newspapers and cardboards, I displace the mulch and add them over the grass then rake the mulch over the papers & cardboards. The initial layers of cardboards have already softened and tear very easily, but the newspapers still hold together. Since the grass underneath has not completely died yet, I plan to add more cardboards & newspapers as I collect them.

Cardboard & newspapers will not allow light to filter through. Clear plastic will. The trapped moisture & light will allow weed seeds to germinate.

The Soil, Compost, Mulch forum offers a lot of practical suggestions in preparing a planting bed. The FAQ is very useful. Please check it out. Here is an example:

Here is a link that might be useful: Creating a new bed without tilling

The clear plastic was mentiond, to 'solarize' the area. In many cases, a clear plastic covering in the area through a summer, will kill bugs, disease, and weeds/grass.