Bucketing FFT into one-third octave bands
For an FFT, your number of data points should be a power of 2. You don't need to capture for a full second, in fact, your update speed will be really slow if you capture for 1 second. If this is a real-time display, the values below give an update speed of 3 Hz, still very slow.
You need to make some compromises. If this is a fun spectrum analyzer, it is not nearly as critical as if you were making a scientific instrument. The lowest bands will have some quantization error. If you are displaying in decibels, this won't be as much as you might think.
My fun spectrum analyzer only performs a 512 point FFT, I had to make a lot of compromises.