The rapid advancement of large language models (LLMs) has highlighted the need for robust evaluation frameworks that assess their core capabilities, such as reasoning, knowledge, and commonsense, leading to the inception of certain widely-used benchmark suites such as the H6 benchmark. However, these benchmark suites are primarily built for the English language, and there exists a lack thereof for under-represented languages, in terms of LLM development, such as Thai. On the other hand, developing LLMs for Thai should also include enhancing the cultural understanding as well as core capabilities. To address these dual challenge in Thai LLM research, we propose two key benchmarks: Thai-H6 and Thai Cultural and Linguistic Intelligence Benchmark (ThaiCLI). Through a thorough evaluation of various LLMs with multi-lingual capabilities, we provide a comprehensive analysis of the proposed benchmarks and how they contribute to Thai LLM development. Furthermore, we will make both the datasets and evaluation code publicly available to encourage further research and development for Thai LLMs.