Boy, that's a tough one. Basically the folks are going to fly once a week, for 2 to 4 hrs (diff. btwn jet and the prop).
That's not a whole lot of utilization for a brand new flight department and they could have some sticker shock....
Not so much the acquisition of the airframe, but fixed costs associated with insurance, pilot salaries, maintenance, hangar, spares, etc...
If it were me, and I was advising, I's say buy a block of charter on Citation for 6 months and see how goes. But to jump in and buy and airframe to do a trip once a week could really put a bad taste in someones mouth when the bills start rolling in.
Since you're talking up to 800 miles, an economical jet charter, say a Citation, will beat the price of a King Air every day at 800 miles.