As much as I like my mini split heat pumps, nat gas is going to be a way less expensive way to fuel heat than heat pumps in this day so a furnace or boiler and air conditioner might be your best friend. (I live in a predominantly cooling environment and installed mini-split heat pumps when gas was more expensive.) If you are going with steam, or some flavor of hydronic for heat, then I'd go mini-splits. An open floor plan is more conducive to mini splits because the more closed-off rooms that you have, the more equipment you have to install. You are way ahead of most people in making the centralized vs. mini split decision since you have direct experience with the latter. If you go with ducts, be sure to put them inside the house envelope, not in a vented attic. If you are going to go with a very efficiently insulated and sealed envelope, the efficiency of the heating and cooling plant don't matter as much. As hot and humid as it seems down on your costal plain, heating is much more the issue than cooling. You might get enough cooling from relatively few mini splits since heat and humidity will move from room to room much faster than in and out of the house if your envelope is good. You might be interested in this recent mini split analysis: Long-Term Monitoring of Mini-Split Ductless Heat Pumps in the Northeast Building America Report - 1407 December 2014 Kohta Ueno and Honorata Loomis

That may be done. Whether it is a good way to go about it is another question. If you can come back with some more detail about the old lake house, you might get a lot of feedback with the advantages and disadvantages of several approaches.

Older lake house with basement and 1st and 2nd floor and no AC. Is it possible to install Central Air on 1st floor and ductless splits on the 2nd?

Seems a bit steep. But there are two systems and it's not clear if there are any installation complecities. For a strightforward installation, though, I don't see why it is this high. Get more estimates. Some HVAC companies charge an arm and a leg for minisplit installations simply because they can.