the project you are describing is not the kind of project where you can get away with inexpensive mics or a poor recording space. when instruments are very exposed in the mix, as in solos, duos and small ensembles, and especially for classical music, you are going to need to get your hands on some decent gear. at the very least you will likely need 3 mics - a pair of neumann km184s or 183s (if you have a good room) for the piano, and something like a schoeps cmc6/mk4 (used out at 2-3 feet for a more traditional classical voice sound) or a neumann U87 (for a more intimate, close-miced setup) for the vocals. i have doen these kinds of things both in live venues and in the studio, and both mutli-tracked and ensemble - each of the methods work fine under certain circumstances. you might want to give us some more information about exactly how you will be recording and what kind of space you have.