Use the same method you used to find the water level to find the bottom. Not that it's important, as long as the water is that high, a shallow well pump will work. The only drawback is that some 2" wells have Bremer Check Valves in the bottom which hold the water up, and you may be getting a false reading. I would find a Pitcher Pump and do a pump test before I started buying equipment. If you find that it produces water with the Pitcher Pump, a shallow well Jet Pump would work fine.
What size depends on how much water and pressure your needing. It also depends on how the well produces.
Pipe size should be carefully thought out. 250' is quite a distance, so 1" or larger pipe should be used. This again depends on the flow required.