Hi Brendan, I would go for practically any organic matter you can find around: (non-stinky) straw, leaves, grass, hay, weeds, avoiding things with seeds as much as possible. As chopped up as possible. Fresh if necessary, decomposed (better) or decomposing aerobically (It's always good on this forum to pay a lot of attention to Dr. RedHawk!!) Don't load it up too much with nitrogen by using for instance all grass clippings.
If you import organic material from someone else's property, make sure they don't use Roundup or similar herbicides, fungicides, etc. Those can really mess things up for you for a long time.
You can also dig out the paths between the beds and shovel the soil into the beds themselves.
The more organic matter you put in the beds, the more they'll settle over time. If your beds have sides, you'll notice this a lot. You will need to do a huge top-up next year.
Make sure the soil in the beds ends up being firm
enough to hold your plants upright!