The orbital period comes from watching the stars, or the periodic variation of their velocity or brightness. To get orbital semimajor axis, you need either the parallax to a visual system or the velocity from a spectroscopic system. In a spectroscopic system, you only have a lower limit unless you know the system tilt. In an eclipsing system, you know everything, including the sizes of the stars. Visual systems should be relatively near the Earth, and have relatively wide separations. Spectroscopic systems need not be near to the Earth, but should have relatively small separations. Eclipsing systems are likely to have even smaller separations (and you have to be lucky). Interferometry is converting some spectroscopic systems into “visual” systems (and resolving the tilt problem).