Ideal Geometric Arrangement of Microphone Array
This will somewhat depend on the spectrum and properties of the signals and what your dominant source of noise, distortion, jitter, non-linearietes etc. are. Ideally you can resolve every point in space with 3 non-coplanar microphones. A very simple solution is one with 4 microphones: one in the origin and three one unit step displaced in x, y, and z dimension. The arrival difference between X and origin pair gives you the x-coordinate, etc. 

You can improve this method by a simple least square approach that takes into account all microphone pairings (6 total). The fit error is metric of how much noise you have in the system. 

Microphone spacing depends on spectral content of the signals you are tracking. If it's fairly narrow band you probably want them to be about half a wavelength apart so you maximize the phase difference between adjacent signals.
A good robustness metric is something like dx/dt, i.e. you wiggle the arrival time a little and see how much the calculated position moves. For almost coplanar microphones that is a large number which indicates that this setup is very sensitive to noise.