I would without hesitation recommend you get whatever is recorded by the Beaux Arts Trio, but I do not think there is currently one in print. So I will blindly recommend Martha Argerich, Gidon Kremer, and Mischa Maisky on DG; based on the quality of those three musicians.
Actually I just searched and found the Beaux Arts Trio performance. It is on one of those discount consumer CDs "Tchaikovsky At Tea Time" on the Philips label. Considering how those CDs are usually put together I do not know if it is the whole piece or just a favorite movement?
Back again for editing. Unfortunitely the Tea Time Cd is just the 2nd movement as I guessed. Look for used or an LP, or go for the DG recording.