I used Blender, it's not CAD but it works well.

The my friend's printer software supported OBJ and DAE that Blender can export directly.

If you're still learning and you don't mind non-CAD softwares I recommend to go for Blender, if you want something simpler there's Wings 3D.

If you need or want a CAD tool, a simpler software you can look at is SketchUp, it's simple and fast to use, it should be similar to TinkerCAD but I never used it so I can't compare it.

3D modelling sure is fascinating, hope to see some pics of your work when you're done!