I suspect it costs more than $1000 to add AC. For AC you need a
compressor and a heat exchanger. You also need to run new electrical
circuits to the outside of the house and freon lines to connect the
two. Can your electrical panel handle the additional load (assuming
you are using electrical power for the AC)? I suspect the cost to be
way more than $1000.

As for the pro and cons, I have had both types. I found hot water
baseboard to be quieter, the heat is more even with the floors being
warmer (just my opinion) compare to force hot air if the ducts are in
the ceiling. The baseboards can limit furniture placement. It is
harder to balance if the system is not properly designed. Pumps do
have to be maintained. Force hot air can dry out the air and you with
it. You might need a humidifer. You will probably hear the fans
running. If the ducts are in the ceiling, you don't have to worry
about blocking vents. It is harder to add zones with force hot air. I
would guess that force hot air would warm a room faster.

Ducts can be easy to run but you need to know how to size the ducts
and the returns. If not properly designed, you could end up with hot
and cold rooms.

Do ypu live in an area where a heat pump would make sense? Worth
checking into.