I'd mix the compost in with the soil, but I'd use the wood chips and leaves as top dressing.

If you mix them in, they'll lose a lot in volume as they decompose. The compost will lose some volume as it continues to decompose, but if it's finished compost, it won't lose nearly as much as the leaves and wood chips will.

Also, wood and leaves mixed into soil can cause a nitrogen deficiency as they pull nitrogen from the soil during decomposition. When they are piled on top, this isn't a problem.

You might research the lasagne method. My roses are very happy!

What you do depends on what soil you currently have. If what you have is a heavy, dense clay (most of Alabama is) then you probably need to one time mix lots of organic matter into that clay. After that one time simply mulch heavily to keep the level of organic matter in the soil at the level necesary.
If you are lucky and have sand all your need do is apply the organic matter you do have to the bed as a mulch and the soil bacteria and fungi will incorporate that for you.