[wiswind]

Well.....first thing that I would want to do with a new to me windstar would be to change the transmission fluid.
The link in my signature will take you to a bunch of pictures that I have posted on webshots of various projects with my '96 windstar.
While mine is different than your 2003 in many ways, the transmission fluid change pictures will be super close to your vehicle.

Your transmission holds 12.25 quarts of transmission fluid, the correct fluid will be one that meets the Mercon V specification.
I usually get 15 quarts to do the fluid exchange....which is what I recommend you do......exchange ALL the fluid.....not just the 6 quarts that you will get if you do a pan drop and replace the fluid you get out that way.

As to the question of if there is more wrong?....that is anyone's guess.......
A transmission repair or replacement need is a common reason for a person to replace a vehicle.
HOWEVER, it IS normal for the motor to "rev up" for a moment whenever the A/C compressor kicks in.
On my '96, the only settings that do NOT have the A/C compressor cycling on and off is OFF, and VENT.
It is for SURE that your A/C will cycle in ANY setting that includes the defrost......as this helps prevent the windows from fogging over on the inside.
The motor will rev slightly whenever the compressor cycles ON.....to prevent the motor from being loaded down.
It is very possible that this is what is happening.
To see if it is.....set the climate control select to "VENT" and see if it happens.
If it does NOT....then it is just caused by the A/C cycling......and NOT a transmission problem.