• Collada (.dae)
• Ogre Mesh (.mesh)

Both can be exported by Milkshape3D fine and easily. However, there are pros and cons for both: The Collada-Exporter is shipping with Milkshape3D, but it does not export animations. If you want to export these as well, you have to download and install the .mesh-exporter. 

Exporting to Collada 

This is the easiest. Just click File->Export->COLLADA and choose a filename for your new model.

How to make Visual3d.net find your new model

Visual3d.net looks for art files (models, textures etc.)  for your game in the games directory. Where you put them there does not matter. You can export a model to YourGame/TestModel.dae or to YourGame/Content/TestModel.dae both will be found fine by Visual3d.net. You are absolutely free to structure your files the way you want. 

Exporting to .mesh

This is a bit harder. First of all you need to get the exporter from the here:
sourceforge.net/project/downloading.php
When you installed it, click File->Export->Ogre Mesh/Skeleton. The dialog shown below will appear.  

Be sure that Export Mesh is checked. I would not generate automatic Level Of Detail since this can be done in Architect as well.
Generating the Edge Lists is unneeded as well.
Generating the Tangents can be done easier in Architect, so I would prefer to leave it unchecked here as well.
If you have any materials you have to check the Export Materials option.
The Export Skeleton & Animation option is fine by default.