I would get a pick ax and dig your hole to the earth, then kick in with a post hold digger. The dimensions of the hole by the post hole digger should be pretty good, I always widen the hole a bit for added concrete.
The hole by the pick ax will be jagged as there is no other "cheap" method of doing this unless you rented a concrete power saw, which is not warrented.
I would sink the post in the ground idealistically 2 feet and then sit the post on a brick. Then fill in with reg sak crete and on the top of the hole, build a cone ramp on all sides, this will shed the water. Not too much of a ramp because your fence slatts will not sit correctly or evenly.
Let concrete dry overnight or if in a rush use "fast set" which will set in an hour or more.
Do not worry about post height, do this after all built, I use a chain saw to do this, much easier and faster.