Go get a Studio Projects C1, or a Rhode NT1 for around $200 for the vocalist, and a pair of Oktava MC012's for $150 each for the piano. On the low end, those are the best investment around.
Of course you'll need a nice-ish preamp that can supply 48v to the mics.
If you start to get serious about doing real recording, you need: a good audio card with decent (as in, better than the sound blaster's D/A A/D) converters. Then a good multitracking application you can run from your PC (like emagic's Logic Audio. Don't get Cubase, Cubase = Rambus) you'll be able to do everything you set your mind to.
Order from
www.americanmusicalsupply.com or
www.sweetwater.com they usually have the cheapest prices, or close to it, and are most helpful in making a purchase. Musician's Friend and Guitar Center (same company now) are hard to deal with when you have a problem with something (I bought a electronic drum set, and ONE pad died after the first week, but they wanted me to ship the whole package back, which I didn't, since it was 100+ pounds) and generally aare more expensive unless you are an ASCAP member.
Good luck. It starts off small, and before you know it, you have 4 racks full of gear.