Basically their are a number of different versions/types of CAD. They are used for a number of different things. such as a engenering CAD could allow you to render how a say engine you built inside of it operates, and even do some virtual testing on the design, but if your trying to go from scratch to a working airplane, you would really need a number of different versions of CAD. And frankly im not sure where you would start, thought the plant would probably be the place to start, as after that you know your thrust, and therefore what kind of speed/friction/gforces the frame and body need to withstand, as well as how much fuel capacity you will need to get x far, take into account weight of all components you want/add into it....yeah sounds like it would be a VERY long process for an individual. not saying it hasnt been done here or their, but generally anything modern like that is done by at least a small 2-10 man team. Be prepared to learn a whole lot of math, several new programs and how to use them.
However if your just looking to take whats in your head and put it on paper to look at so to speak even if its not feasable/tested. then a rather basic version of cad would be needed and then you just need a PC powerful enough to render it, which in that case isnt much nowadays.