The "easy button" would be steel posts wrapped with what ever flavor of wood you prefer. Not sure where you are located. However, based on the link above, assuming east of Mississippi. Woods I would consider for your project:
1) White Oak - By far the strongest, most weather resistant of the hard woods in the eastern U.S. "Closed cell", so will not soak up or transmit water. Think oak staves in bourbon barrels. Think sill plates in covered bridges with continuous ground ground contact for decades. Not cheap, but nothing better in the eastern U.S. I would bet that you could find a custom sawyer within half a day travel distance who could source and saw out white oak timbers to your spec for significantly less than the prices noted above. ForestryForum DOT Com has a list of custom sawyers across the U.S. that might be a starting point.
2) Cedar - Need to differentiate between Eastern Red Cedar and Western Red Cedar - I am only familiar with the Eastern variety. The red heartwood is very rot-resistant. And very pretty. Might be difficult to source the size pieces you are spec'ing. But not impossible. Richard Newton at CedarUSA DOT com in Marengo, IN could provide some insight on availability and pricing.
3) Sacrilege to some on here, but Black Walnut - Strong. Nearly as rot-resistant as White Oak. Was used as a substitute for white oak in covered bridges when white oak was not available. And contrary to popular belief, not every walnut log is a $1,000 veneer log. The scruffy walnut logs that I sawed into trailer decking for my lawn mower trailer have lasted 11 summers so far, versus the original treated pine lumber that had to be replaced after 5 summers.
4) Cypress - No personal experience. However, my understanding, it is frequently used in Southern U.S. for outdoor projects. Should not be a problem to find the size pieces that you are looking for.
Sorry for the long winded post. Regardless of your wood choice, Good Luck with your project !