3D object modeling that can change whenever the option is being clicked

I am planning to build a website which would show 3D model image of a product with customization. For example: I have list of furniture(Example: chairs, tables, desk) Then when the button is clicked it will show the 3D image. The idea of my project is that every time the user clicks on the option given in the left navigation it would promptly change the 3D image design. Is there a possible software to use for this? for free? My instructor told me about unity and autodesk software, i have a no knowledge on making 3D design but can someone humor me about this kind of stuff? Or any recommendations? hmmm