James, lets go back to your original question, which plane?
There will be no perfect plane for all missions but your mission profile is interesting.
#1 any turbine will do that, C90, Cheyenne II what ever
#2 Same as #1
#3 A little more problamatic. It will take a fuel stop and will use up a day each way. That may not be a problem but needs to be considered.
#4 You are going to be crowded. Especially since you are going to be operating with two pilots for at least a year. A B200 comes closer to accomplishing all 4 missions. Any of the Cheyennes are just to small for mission 4
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Remember that the missions were ranked in order of importance. Also #4 is with my wife and kids who are 9, 7, 5, 3, and 1. I know they will be growing, but we're not talking serious heft for several years. I also included myself as one of the pax in all scenarios.
Expectations:
#1 I respectfully disagree here. You will not need a CFI but you will need a babysitter. I suspect with a 9 place airplane the minimum will be 2000PIC, instrument/commercial, approved initial training and yearly recurrent and 200 hours in make and model with the babysitter. Here I am just guessing based on my personal experience. What you are willing to pay for insurance and your requirements for liability coverage will largely shape this.
#2 Not sure what is meant by "on site". Training requirements addressed above
#3 In most small corporate flight departments the pilot manages the plane. Part 135 standards will substantially increase the cost. Parts can not be used "on condition". One example: At five years since overhaul the props only have 900 hours. Must still be overhauled can not be IRAN'ed. Many items on turbine aircraft have an hour limit that must be met for part 135 rather than inspected and return to service on condition. Just something to consider. I am just guessing here but could increase DOC 20-30%, perhaps more.
#4 It is what it is. Never heard an owner complain about the plane being too fast or able to carry too much weight.
#5 FIKI is assumed
Other:
#1 You already see that Ted and I disagree. You will have to look at the market and see what is out there. I think the B200 fits your mission profile the closest but, you do have options.
#2 I do not think this matters because I don't think there is a piston plane that you would be happy with.
#3 The tough one. I threw out a number of $1300/hour on the IIIA at 200 hours per year. Airframe parts, especially on orphan aircraft like the Cheyenne are horrendous. The basic turbine engine, compressor, hot section, and gearbox don't give much trouble as a rule. But when they do.... A couple examples: If you eat a gearbox on a 200 you will not get out for $100K. A hot start? One set of turbine blades for our -61 is well north of $75K, that is just for one set of blades, no labor and each engine has three sets. You get my drift. Again it is rare but....
These are the things I would factor in if I were making the choice and decision on whether to buy a plane. There will be some here who disagree and their oppinion should be factored in as well. There will not be a perfect answer nor even a perfect plane. JMO
We are on the same page on all points. This would be primarily a business use aircraft and that is what is driving the purchase. I think the most realistic scenario is to end up paying someone to manage the aircraft, whether that be a local FBO(I'm close to a mid sized field with good mx including turbines), or a full time pilot. Only wrinkle is that I want to learn to fly the thing safely and eventually solo, however I will always want to keep the option of sitting in the back when situation calls(or I'm shot).