Which capacitor to choose for ACS709 to filter 50Hz noise?
You're thinking along the right lines but you obviously have no experience with mixed analog/digital systems. "amount of measurements per second" has a name : sample rate. 

And there is a very well known relationship between analog bandwidth and sample rate called the Shannon (or Nyquist) Sampling Theorem. Searching "sample rate vs bandwidth" should set you on the right path to finding much more information should you need it.

Choose a sample rate - you already have.

Choose a suitable bandwidth to match that sample rate.
I'd keep it simple and choose 0.5Hz for 1 sample/second, giving a sample rate exactly twice the bandwidth.

Choose a capacitor to give that bandwidth.