Consider the whole plot. You have raised beds. The paths are lower and probably (puddled by walking) poorly draining. Do you have any fall upon the site, ie is one end/side lower to allow the water to escape?
Wood-chip material is considerably cheaper than bark. Often free from a local tree surgeon , who, for a couple of ‘pints’, will probably tip you a load as required.It is easy to lay, to keep weed free, and eventually will compost(3 seasons?) to a rich brown mulch.It will also float: so needs keeping in place by consolidation. If you can allow for a drain from the lower area, it will remain relatively tractable all season. It will hold large populations of worms, it can also have leaf material added, which may take 2 years to rot away. After 2 years it may be sieved as a compost material, retaining the finer parts. If the paths have grass cover, or no noxious weeds, lay card before applying. I try to lay 4″ layer on card.
Be prepared for a considerable display of fungi; possibly edible but seek competant advice.
