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Laser induced cavitation is one of the effective techniques to generate controlled cavitation bubbles, both for basic study and for applications in different fields of engineering and medicine. Unfortunately, control of bubble formation and symmetry is hardly achieved due to a series of concurrent causes. In particular, the need to focus the laser beam at the bubble formation spot leads, in general, to a conical region proximal to the light source where conditions are met for plasma breakdown. A finite sized region then exists where the electric field may fluctuate depending on several disturbing agents, leading to possible plasma fragmentation and plasma intensity variation. Such irregularities may induce asymmetry in the successive bubble dynamics, a mostly undesired effect if reproducible conditions are sought for. In the present paper, the structure of the breakdown plasma and the ensuing bubble dynamics are analyzed by means of high speed imaging and intensity measurements of the shockwave system launched at breakdown. It is found that the parameters of the system can be tuned to optimize repeatability and sphericity. In particular, symmetric rebound dynamics is achieved almost deterministically when a pointlike plasma is generated at the breakdown threshold energy. Spherical symmetry is also favored by a large focusing angle combined with a relatively large pulse energy, a process which, however, retains a significant level of stochasticity. Outside these special conditions, the elongated and often fragmented conical plasma shape is found to be correlated with anisotropic and multiple breakdown shockwave emission.