Atmega328 and ADXL335 - is the right choice for vibration analysis?
First of all, 3000 RPM is only 50 Hz, so sampling is not a problem for the fundamental frequency.  But you usually want to see harmonics, to pick up gear tooth issues, etc.
I suggest using my Daqarta software with a sound card to do your initial testing.  It already does everything you need, including waveform, spectrum, and spectrogram displays plus a lot more.  You can use it free for 30 sessions or 30 days, then the sound card inputs are no longer supported.  By that time you should have a good idea about what you need.  As it turns out, Daqarta also supports Arduino, and that does not end with the trial period.  So you may be able to do everything with an Arduino, for free.  The Daqarta site also has a contact page, and I am glad to answer questions and provide specific help for any issues that arise.  That include free users.