Interest in the study of next-generation underwater sensor networks for ocean investigations has increased owing to developing concerns over their utilization in areas such as oceanography, commercial operations in maritime areas, and military surveillance. Underwater acoustic communications (UAC) network channels are fast-varying (spatially and temporally) according to environmental conditions. It is tempting to use adaptive modulation and coding (AMC) for UAC networks to improve the system efficiency by matching transmission parameters to channel variations. This paper focuses on analyzing a measured sea trial dataset by using a rule-based strategy (i.e., three-dimensional analysis, modulation-wise analysis, and a fixed-SNR strategy) to find the suitable link adaptation procedure depending on the channel quality. Hence, we plot a scenario of the measured UAC network data rate vs. Signal to Noise Ratio (SNR) and/or Bit Error Rate (BER) to pick the best AMC combinations in the context of adaptivity to the channel. Due to non-reversibility limitation of rule-based strategy, the work further extends to use machine learning (ML) algorithms to classify the MCS levels by investigating the channel characteristics. Boosted regression tree, from among the four ML algorithms we adopted for the analysis, shows formidable accuracy of 99.97% in classifying MCS levels. This ensemble of trees learns from the uplink data of the buoy and the base station and relates the MCS levels to channel metrics and signal characteristics especially subject to SNR and BER constraints.