How much sun will these beds get before trellis?
Assuming full sun, here's how I would do bed 1, FWIW.
I have had good luck with three sisters corn, pole beans, and watermelon. The traditional method used by the native American Indians was corn, beans, and squash but I find substituting watermelon for squash works well also.
Plant the corn first then after it is up a few inches plant the pole beans in proximity and watermelon/cantaloupe "mounds" on each end outside the corn to enable the vines to run along with the corn but get full sun on the mound itself. You could do a watermelon mound with 4 or so plants on one end and a cantaloupe mound with 4 or so plants on the other end. I would dedicate one 3x8 bed to that set-up with three rows of corn, one on each outside row and one down the middle with something like 8–10-inch spacing on the corn plants.
In bed 2 I would do the following:
Plant your seed potatoes about 12 inches apart in two rows equally spaced in the bed. Plant sweet peas in between each seed potato after the potato begins to break through the soil. These make excellent companion plants, and I have been planting in this manner for many years. The peas will provide some nitrogen to the growing spuds.
Then in bed three, plant three equally spaced rows with one row each of carrots, spinach, and lettuce respectively.
Just a suggestion...with no need for the cattle panels. If I was using the cattle panels, I would only do so on bed 3 and plant cucumbers to train up the panels on one side that minimally blocked sunlight.
That's just how I would do it...not intending to say how you should do it.
