Use 2x4 verticals into the stake pockets. Get two sheets of interior plywood 3/8" or 1/2" thickness. Rip both sheets to 24x96; cut one in half to 24x48. Screw the plywood panels to the uprights and scab on 2x4 blocks at the corners and bridging the 2 sections (8'+4') on the sides. Cut one section down to 6' for the front.
You will find that branches cannot stick through the plywood and make it difficult to unload.
Before you load the trailer, lay a length of chain in the bottom of the trailer. If you can tie it off, the trailer can be unloaded quickly by just driving the trailer out from under the load. Then pull the chain out one side and take it with you.
I have done whis to raise the bed height of my pickup by extending the walls above the sides with plywood. When I am done hauling, I unscrew the plywood from the 2x4's. My 2x4's are whitewood rather than pine to save weight.

In this situation I would use nothing but pressure treated wood, and from a better lumber store.
The big box stores seem to sell a lot of junk wood.

I've had good results with 1/2" pressure treated plywood treated with an opaque stain designed to use on green-treat wood.

My experience with the Menards big box stores here in Minnesota is that their lumber quality varies from unusably poor to the best you can find anywhere. If you are able to go early in the day, and especially on weekdays, you can sort through a pile and pick out good lumber at a discount price. I wouldn't trust them to deliver wood I hadn't personally inspected.

I've framed out sides for two trailers over the years. Mine had angle iron rails about 8" above the floor. My solution there was to make 32" sidewalls out of 3/4" exterior plywood (can't figure out why an earlier replier would use interior ply!) and frame the perimeter with pressure treated 2x4's. space vertical 2x4's about every 3' and toenail all joints with exterior deck screws. As far as attaching the walls to the trailer, you could use your stake pockets by running the vertical supports long enough to utilize them. In my case, I bought J bolts and washers through the bottom framing & plywood to hook onto the angle iron rails. With this connection, I can remove the walls in 5 minutes when I need to. To keep the walls in line, I screwed cleats to the floor inside the walls. To hold the front corners together, you could use L brackets, but I ordered corner braces for trailers from Northern Tools. They're interlocking and secure tightly, but unhook easily with an upward lift on the sidewalls. Hope this helps!