There's a lot more to making a half-decent recording than just the mics. You need some sort of preamp (that at least needn't be expensive) and a recording device with decent frequency response and MANUAL GAIN CONTROL. If you record with anything that has automatic gain (level) control, the sound will never be any good at all. ALC is designed for recording speech to dictation-machine quality, nothing more.
Behringer kit offers astounding bang for the buck, as cheap stuff goes. None of their stuff is top quality but I've never found a bit that didn't do pretty much what it says on the box. You could do worse than Behringer mics, Behringer preamp, and a sound-to-computer interface such as those made by M-Audio. Maybe Behringer also does that kind of thing these days too. It's a cheap option and can be perfectly respectable quality.
As for microphone positioning, in a domestic room I'd put the mic anywhere except in the piano. I get quite decent results recording my Bechstein grand with the lid shut (completely shut) and the mic pretty much anywhere in the room. Not great recordings, obviously, but clearly piano-ish which is about as much as you can hope for. Mic in the piano is strictly for when you want to make the Elton John extra-bright-on-stage sound.