[...] should I turn it to the calibrated profile that I am currently using for my monitor?
Yes, just check the box and select your monitor profile in the list. The conversion is not performed twice as nothing really happens when you set a monitor profile in control panel. This is just a place where applications can go look for your preferences (and you can put multiple profiles in there, by the way), but the actual conversion really is handled by the applications. Now, if you use some special software that loads with Windows and runs at all times to "color manage" your desktop, you might want to make some tests. You could use Photoshop as reference, and you should get exactly the same rendition in FPV if everything is working and set as it should.
You can get small images with esoteric profiles from this page
(ICC website), just right-click and save them, they are useful to find out if CM is working as it should with any app.
Hope this helps,