Hi. Welcome to Just Answer.

You can just use 2x4s for the posts. the reason for 4x4 posts is the wind factor. A 4' fence in 40 mph winds will snap a 2x4 easily. An 18" fence will not have that concern.

QAs for the depth of the posts if you match the height of the fence plus a bit you cant go wrong. If you gat 2x4x12' legnts of lumber you will get 4 pieces at 36" long. As the posts will sit a bit lower than the fenc it will take the depth to 24" +/-. If you concrete the posts in they will last a lot longer than just packing dirt around them.

The best way to do it is to set all the posts in the holes using a tight string line to align them and set the height. Make a mark on th estring line with a black marking pen where you want each post (4'centers). Have someone set the post in place ans plunb it with a small level. Pour some quick crete post mix around it keeping it on the mark and plumb. Once you have enough post mix in to hold it in place tamp it down with the end of a shove handle. Fill it up to within a few inches of the top and then fill the rest with water. The water will wet the concrete and activate it in place. Allow it to set overnight and then build the fence between the posts.

You can use pressure treated lumber or just apply a few coats of Jasco Wood Preservative to standard lumber up to about 3" above the ground level. Paint as desired and you got a nice fence that will last many years.

If you would like any additional information or have more questions please don't hesitate to ask!

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