We show that distributed Bragg reflector GaAs/AlAs vertical cavities designed to confine photons are automatically optimal to confine phonons of the same wavelength, strongly enhancing their interaction. We study the impulsive generation of intense coherent and monochromatic acoustic phonons by following the time evolution of the elastic strain in picosecond-laser experiments. Efficient optical detection is assured by the strong phonon backaction on the high-Q optical cavity mode. Large optomechanical factors are reported (similar to THz/nm range). Pillar cavities based in these structures are predicted to display picogram effective masses, almost perfect sound extraction, and threshold powers for the stimulated emission of phonons in the range mu W-mW, opening the way for the demonstration of phonon ``lasing'' by parametric instability in these devices.