Use 4x4 or 6x6 material. The best way to join the vertica to the horizontal is to use a half-lap joint. Do a search online for half lap joints and it will be pretty self explanatory. You can do it with a circular saw by making a bunch of saw kerfs and removing the material, then cleaning up with a chisel. Exterior wood glue and a few screws and you're good to go.
Set the post in the ground and compact the soil around the post very tightly. Add a little concrete if you want it more permanent.