Do they by any chance sell coldfusion hosting? If they do that is why they will be pushing it on you as then you get tied into their hosting aswell (not many people can host coldfusion)
I have worked with coldfusion in the past and tbh it is nothing special. It is no better than php or asp. I inherited a site that was designed in it and it didnt take long to pick up the basics as will all programming languages they are similar in a lot of ways. However it does give a lot of drawbacks on hosting. Mainly because not many hosts provide coldfusion and when they do the packages are expensive an under spec'd. You are right in saying it needs some server side software, this runs into multiple thousands of pounds to purchase hence why not many hosts do it. If you have the option between the three, coldfusion, asp and php, i would choose php every time. However i wouldnt rule asp out of the question if this is your prefered language.
As an example with coldfusion hosting you would look at paying 10x more a month than you would with php or asp.
Also with php and asp you are more likely to find answers to any problems as more people use it.