Is there a rule of thumb to choose an aircraft for long-haul operations?
Because airplanes are incredibly expensive, using a "rule of thumb" would be extremely foolhardy.

A detailed analysis, likely laid out on a spreadsheet, would be much more appropriate.  You did hit on many of the major points, which also include:


Aircraft Range
Passenger Capacity
Speed
Crew Costs
Fuel Consumption
Cost per hour
Other costs: Insurance, Maintenance, and Leasing
Runway and Weight limitations
FBO services available


Obviously, if a candidate plane cannot fly the desired distance (perhaps limited by range, ETOPS, altitude or runway at takeoff or arrival), then you can't use that plane.  If a candidate plane cannot carry enough pax or cargo, then cross that off.

But once you have planes that can actually complete the mission, then its down to a complex matrix of costs, speed, time, and other benefits, and is a maximization problem without a precise answer.  (Some people will value speed above all else.  Some will value comfort and amenities.)