Recent advances in table understanding have focused on instruction-tuning large language models (LLMs) for table-related tasks. However, existing research has overlooked the impact of hyperparameter choices, and also lacks a comprehensive evaluation of the out-of-domain table understanding ability and the general capabilities of these table LLMs. In this paper, we evaluate these abilities in existing table LLMs, and find significant declines in both out-of-domain table understanding and general capabilities as compared to their base models. Through systematic analysis, we show that hyperparameters, such as learning rate, can significantly influence both table-specific and general capabilities. Contrary to the previous table instruction-tuning work, we demonstrate that smaller learning rates and fewer training instances can enhance table understanding while preserving general capabilities. Based on our findings, we introduce TAMA, a TAble LLM instruction-tuned from LLaMA 3.1 8B Instruct, which achieves performance on par with, or surpassing GPT-3.5 and GPT-4 on table tasks, while maintaining strong out-of-domain generalization and general capabilities. Our findings highlight the potential for reduced data annotation costs and more efficient model development through careful hyperparameter selection. We open-source the project and our models.