I work for a consultancy, and for us it's Y under 1,600 miles and J above that. Used be a four-hour cutoff but that got gamed. Also for non-chargeable travel over 1,600 miles, Y+ is "encouraged".

As for choosing airline and time, staff members are permitted to use their professional judgment, but the lowest offered fare for your journey (within 3 hours either way) is printed on your itinerary and occasionally people get pulled up and asked to explain a choice.

As for miles, a don't ask, don't tell policy applies.