Black poly is the normal thing. Read the label carefully, there is stuff that isn't for drinking water, there are also 2 pressure grades. You likely won't need much pressure, but it has to do with how durable the pipe is.... Sure is better if you burry it some, here we go 5 feet for freeze protection, sounds like you aren't here tho!
There is a blue plastic pipe now that is thicker walled, much more durable, that most folk are using for water lines now. Good tough stuff. I would use that, but I hate having re occurring problems later on with leaks and all.
The farther water has to travel in a hose, the more resistance it has.
So size of the hose depends on the pressure it is getting (gravity feed?) and the distance it has to go.
At least 3/4 inch, and a gravity feed 500 foot setup you might want 1.5 to 2 inch depending on what all you are doing with the water.
Paul