The best free 3D modeling program is probably Blender. It's kind of tricky to learn, but there's a lot of good tutorials and other resources on the site.
Unity understands Blender's file format, .blend, natively. You just have to drag a .blend file into the project, and it's ready to go. The one exception is that texture images will need to be re-applied to the model. But that can be as simple as dragging the image onto the object.
I've had some success exporting to the .FBX format, as well. This preserves the textures, though I haven't had 100% success with it.
You can import unlimited assets, in any version of Unity. I don't know about the Standard Assets, though. Share CG seems to be pretty good for getting free models, but I haven't used it before personally. There's also 3DM3. You can find a lot of them just by googling "free cg models".