First – obviously, sound starts at the instruments. Rich, classical sound pretty much requires at least a decent baby grand. If you only have an ordinary upright piano, no miking can really get you there. Similarly, the room acoustics have an enourmous influence: any square room has nasty resonances, and even if these are hardly noticeable while you're playing they'll become painful on a record with substantial room component, as you'd generally want for a classical recording. Take that into account before spending any money on mics – of course those are important too, but rather less than instruments and rooms!
For the microphony, the simplest good option is to use an ordinary stereo-pair of microphones. Place it somewhere audience-like to get a natural, not too lop-sided stereo picture. I would also record the violin with the very same mic setup, to give a “realistic live-like sound”. The stereo configurations I'd consider are
M/S. Gives you a clear center signal, and easily controllable stereo width / room-content. If it turns out the room sounds just too bad, you can reduce the side component and replentish the reverb with digital convolution of a well-sounding hall. Note that you need a figure-eight mic for this; ideally use two large-diaphragm mics, one cardoid and the other fig-8. You'll need to spend at least 300$.
ORTF. Nice wide stereo picture even if the piano is not so full-bodied – provided the room sounds good. This technique works quite well with most small-diaphragm condensers, they just should be matched. It might sound a bit distant/feeble though.
An alternative approach would be a close X/Y pair, pointing right into the lid or even on the hammers. This is often used for pop recordings because it gives very crisp attack that won't drown even in a loud mix with drums (and no reverb smearing – save for the piano's own sympathetic resonances); but for classical recordings it is rather too harsh, in particular if the piano doesn't sound that smooth. Also, the stereo image sounds a bit synthetic with this technique, and you'd need to record the violin with another mic position, which needs to be compensated for in the mix. I wouldn't recommend that to a beginner.
If neither the piano nor the room has convincing acoustic properties, you might be better of not recording acoustic piano youself at all. Digital modelling / sampling has become really a viable alternative by now, for instance Pianoteq.