Is there a rule of thumb to choose an aircraft for long-haul operations? Are there any rule of thumb for a  NEW commercial airliner, maybe 200 seater or more, for long-haul operations ? I imagine it would be -


mostly bigger aircraft as amount of fuel needed would be more
amount of food needed would be more
amount of waste generated would be more
discounts offered by manufacturer 


all of which points to having bigger aircraft. 

Apart from approximating number of passengers either between A or B or A - hub what sort of other factors influence what sort of aircraft would it be. 

I am using long-haul definition from Wikipedia

To make it more precise - 200 or more pax.
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.)