The smallest recommendable distance would be a minor third, or 3 semitones apart. This is also commonly used in sampling musical instruments efficiently, as each sample is pitched at most 1 semitone away from where it was originally recorded. On the other end of the spectrum, things like octave jumps (12 semitones) obviously aren't ideal. Ultimately, it depends on the tone of your voice, and the way it changes as it travels up and down your comfortable singing range. If you have a dramatic change in tone (ex. from head voice to falsetto), it's okay to record something as small as 1 semitone away.
At the least, try to record a pitch in the middle of your range, at the bottom of your range, and the upper-middle of your range. Resamplers generally do a better job changing the pitch upwards than downwards, so you'll get better results recording at a pitch a bit lower than the range it's meant to cover.