Hi,
With your budget i don't think you will be getting to Miami let alone New York ( with the G200,CL604) without an fuel stop which may add a bit of journey time but seen as your travel purpose is leisure rather than business it need not be as bad , In addition without looking at an abundance of factors a plane with a smaller range generally has a lower operating cost.
If you do look for a plane with 3800nm+ range you should ask yourself does the extra range really match what your typical missions are is the extra cost of the aircraft and ongoing cost of the aircraft worth it for 12 trips a year to Europe. There's a clear conflict of interest if a) you want a luxury long range private jet but b) you don't want it to be a wallet killer.
As you don't want something that's an wallet killer the worst case is buying a plane that you can't afford to operate - I think the Hawker 900 or Hawker 800XPR is ideal it will take longer to get to America or Europe due to more fuel stops but it's operating cost will be considerably less. The G200 you mentioned will do the same as the Hawker 900 but get there a little quicker and have an larger cabin but the operating cost will be soo much more.
Reading back through my post it appears a little loud but that is not my intention.