Recent advancements in foundation models have sparked interest in respiratory audio foundation models. However, the effectiveness of applying conventional pre-training schemes to datasets that are small-sized and lack diversity has not been sufficiently verified. This study aims to explore better pre-training practices for respiratory sounds by comparing numerous pre-trained audio models. Our investigation reveals that models pre-trained on AudioSet, a general audio dataset, are more effective than the models specifically pre-trained on respiratory sounds. Moreover, combining AudioSet and respiratory sound datasets for further pre-training enhances performance, and preserving the frequency-wise information when aggregating features is vital. Along with more insights found in the experiments, we establish a new state-of-the-art for the OPERA benchmark, contributing to advancing respiratory audio foundation models. Our code is available online at https://github.com/nttcslab/eval-audio-repr/tree/main/plugin/OPERA.