I use a tiller on the back of my tractor to till up new ground. I go over it one time, let it set several days and then go over it again. I do the same thing when i'm reclaiming old pastures/fields, except i use a much bigger tiller for those.
As for mulch, i pile it on EVERY year, and i have been growing gardens this way for years and years. I plant the garden and start mulching,
If you have weeds comeing through the much, then your mulch isn't on thick enough!
Pile it on, you can't put it on too thick, it will dry out and nothing will grow through it,
And the plants grow like CRAZY, use less water, produceing VERY well,
In the fall, i till it down, and if becomes food for next years plants.
DM