Actually it's the 'slicer software' which will add support structure if you tell it to. I usually design my own supports into the object I'm creating because the 'slicer software' tends to overdo it.
Btw, many thousands of items have already been created by others. Do a search on a site called https://www.thingiverse.com/ and download the .stl file of your choice. The slicing software usually comes with your printer and open source versions are available. The 'slicing' software creates a .gcode file which the printer uses to print the item.
There are several free 3d design software packages you can use; 123D Design, Fusion 360, SketchUp, and etc. Check out https://www.tinkercad.com/ for a simple, easy to use online 3d cad designer which has tutorials to get you quickly creating 3d designs. The Tinkercad site also has many 3d files for download, created by others. The other applications all have tutorial videos available on Youtube.
Thanks for the suggestions. Now I need to figure out which 3D printer to buy.