My preferred way of recording a piano/vocal performance is to use two condenser mics, preferably a 3 inches from the strings or if it's a upright piano, just mic the back of the piano.
It's a good idea to use some baffling. A large piece of foam or anything that blocks the path of the piano bleeding into the vocal mic is preferable. Simply place it where the sheet music would go.
Then use a directional mic, something like a dynamic mic which will reject more of the piano bleed.
Keep in mind that this is a live performance, so treat it like a live performance. And most importantly...it's about capturing a great performance before everything else.
