I put 30 6 inch posts for my dog yard a few years back, I used a 12 inch so that I could jam rocks on the sides of the post down 36 inches..
I finally bought a "post hole digging/tamper bar". It's a serious 6 foot pry bar (weighs 20-30 lbs?) that I use for about everything else besides post holes, but it is great for tamping the dirt along the side of the post at every level as you fill the hole back in. Once your done the post is wicked solid compared to just stomping the surface level dirt around the post.
If you want three posts to be in a perfect line, one of them is going to need some modifying with a clamshell digger. The more you put in, the more that you will need to modify. I have a six and a 12 inch auger. The six inch is worthless. Just realize that the smaller hole you drill with your tractor, the more work it will take to modify it so the posts line up by using the clamshell digger. Be sure to get the very best that you can find. My favorite one is all metal and twice as heavy as the wood handled one.
Looks like I can get a PhD w 8 inch auger at a good price. So looks like that should suffice.
Posts will have 1 bag quick Crete dumped in hole and then filled w dirt.
If you want three posts to be in a perfect line, one of them is going to need some modifying with a clamshell digger. The more you put in, the more that you will need to modify. I have a six and a 12 inch auger. The six inch is worthless. Just realize that the smaller hole you drill with your tractor, the more work it will take to modify it so the posts line up by using the clamshell digger. Be sure to get the very best that you can find. My favorite one is all metal and twice as heavy as the wood handled one.