Not sure exactly what your asking.
Are u planning on tracking the piano and your voice same time with one mic set up?
It is a bit confusing as some use LAv on pianos for up close mics, and of course could be one on you for the vocal.
If you trying to capture piano (acoustic) of any decent quality, I would highly suggest a stereo pair of mics. As for the windows movie maker, even if it did no way to make true stereo from a mono source, it would be putting the mono in two channels, which is not a LR stereo image.
TO reduce outside bleed from the outside noise, yes close mics will be the way. Upright, Either stereo mic into the top of the piano or two behind the sound board.
I don;t suggest Lav for piano, but some get nice results with DPA Lavs.
It is difficult to know our setup and how many mics you could potentially have access too.
Not saying you could;t do this all with one stereo set or even one mono mic, but getting the proper gain on the vocal and coaxing a nice sound from the piano from these singular sources, will require perfect mic placement and still be a challenge and the vocal might never sit right with the piano.
If you let us know what mics you have access to, how many preamp channels, upright or grand, what kind of quality of vocal and piano are u looking for?
Is this a video camera?
Shotgun mics are popular for video, as they are very directional and reject at good deal of outside noise. Not sure again your exact application and environment.