I have recently purchased a 3,600 sq ft Ranch style home in NW North Dakota. We have hot water baseboard heat and believe it to be very cost efficient way to heat in this kind of climate ( negative 40 in the winter to 110 in the summer). Which brings me to my question what would be the best and less expensive way to add air conditioning to my house. Also we have an unfinished basement.

I would look into split unit ac systems. They mount on the wall and the condenser sits outside. You will most likely need two or three of them to keep a house of this size comfy. These systems do not require any ductwork, and work very well. If you would like more info on them, please let me know.

With an unfinished basement, you could also have and air handler installed, but it would require installing ductwork. I really think your best bet would be mini split system. Let me know what you think.

Do you have a ball park figure on each of these setups.

Sorry, I can't give prices here. It all depends on if you are having them installed professionally, or doing it yourself. Either way, you will have to do some research and find the best price. It would be impossible for me to give you an installed price without being there to see your layout. Units themselves vary in price. All I can recommend is talk to some local hvac shops and see what they recommend. Most of them will give you free bids. Good luck.

If I were to go with the air handler unit, what would I need. Also would that be a stand alone unit or would I have to change over to forced air.

I am not familiar with the system that you have but I have add chilled water cooling to a couple of homes with hot water heating. I think it would be well worth you looking ito it.

If I were to update to chilled water what does that usually entail.

You would just have to get a local Tech to bid a job like that for you.

Call someone and ask for a free bid, and even a second.