I have had raised beds for years and the general mix Mel recommend is fairly common in raised bed gardening. Truly, the mixture needed depends on where you live. The primary objective is to keep the soil from compacting so your crops can grow...spread their roots so to speak. Till that bottom to try and kill any weeds and grasses growing and lay garden cloth to inhibit any further growth. You will need some additional additives besides your compost and I have found potting soil works great as well as the bagged raised bed soil. One thing I did was put red wigglers (worms) to help keep the soil from compacting.

I am pretty much organic and even with raised beds still pull weeds occasionally. My beds are considerably taller than yours, thus not as many weeds. I have one short bed about the height of yours and have more problems with weeds in it. Even so, you have less problems than in ground gardens do. The black plastic over them is a good idea to help.

If you add fresh manure, make a tea and water with it. Fresh manure is hot and can burn your garden. It needs to lay out for a time to mellow. Know several who swear by gin trash too but I have never used it personally. I redress my beds annually with about the top three or four inches of soil. By the time things settle and you pick crops, you tend to lose a few inches each year.

Also, remember to rotate your crops so the same plants are not in the same beds annually. Lastly, ants tend to be a problem with raised beds, so pay attention to that. Wishing you great success. There are a few threads around showing my beds. Fortunately, I have had great success and hope you do too. One last thing...your pics look a bit on the shady side, so be aware of how much and where your sun shines and plant accordingly.