Hammamatsu has a wide variety of photodiodes. I recommend using a PIN photodiode, as your "string" is going to be vibrating pretty fast. You can use it for both frequency and velocity (Doppler) measurements. You didn't say which parameter(s) of your vibrating string you are actually measuring...
Almost any silicon photodiode will have good sensitivity at 0.63-um, you just need to check the data sheet. A string has both length and diameter - so please give both, and if possible the expected fundamental frequency and number of harmonics you are interested in. Europium is right that HF sensing is easier in principle with PIN photodiodes, because of their low capacitance, but my guess (knowing nothing about the string) is that you will be looking at quite low frequencies (<200-kHz), and have lots of light available, so this should not be too problematic. If you are imaging the string onto the photodiode to look at the mode patterns, you may wish to use a split field and have your diodes in pairs.