« If you want a high-quality low-budget piano... »

... this is your instrument. The Yamaha P-85 has one of the best piano sounds that I ever heard. Other sounds are very good too, but the acoustic piano deserves to be highlighted. The P-85 can be used by all kinds of pianists, from beginners to professionals, in nearly all styles, from classical to jazz, also rock and blues. And the best thing is that it's not expensive.
It has a downside, though: no Line Out jacks. You have to use one of the two frontal Phones jacks - I recommend using a Y cable with one stereo banana plug on one side and two mono banana plugs on the other, so you'll not lose the integrity of the sound. But it may be not a problem, actually.