In this study, we examine the statistical properties of speckle patterns produced by the scattering of Hermite-Gauss beams (HGB), Laguerre-Gauss beams (LGB), and Bessel-Gauss beams (BGB). We have considered entropy, speckle contrast, skewness, and kurtosis as the evaluation parameters for statistical analysis. It is observed that the entropy is increased by increasing the transverse modes of HGB, radial index p, and topological charge l in the case of LGB and BGB speckles, whereas the speckle contrast=decreases with the increase in transverse modes number of HGB and it increases with the increase in radial or azimuthal indices of LGB and BGB. The positive skewness has been observed for all the modes which is attributed to the existence of large dark points in the speckle patterns, which is being confirmed as well with the distribution plots. It is also observed that these speckle patterns have a very high value of kurtosis compared to the Gaussian profile, for which it is close to 3, which indicates the high randomness with the increase in radial and azimuthal indices. We have experimentally captured the speckles by scattering HG, LG, and BG coherent beams through two distinct ground glass plates (GGPs), i.e., GGP1 (Thor lab DG 10-120) and GGP2 (Thor lab DG 10-220). The statistical analysis presented in this work will make it easier to distinguish between the structured beam speckles in various fields, such as optical information security, optical imaging, free space communication, metrology, and other related fields.