3D model modifier embeded in website

I am building a furniture website that also sells custom furniture.

I want to have a section in the website where visitors can choose from a variety of options such as dimensions, material, handles, etc. and have a 3D model update as they go along.

There would be too massive amount of 3D models we would have to generate if we simply tried to make one for every combination of options.

So my idea is to use a program to build a base model that can be manipulated in those ways by user input.

So simply any suggestions?

Thanks in advance for your help.