An ideal speech recognition model has the capability to transcribe speech accurately under various characteristics of speech signals, such as speaking style (read and spontaneous), speech context (formal and informal), and background noise conditions (clean and moderate). Building such a model requires a significant amount of training data with diverse speech characteristics. Currently, Indonesian data is dominated by read, formal, and clean speech, leading to a scarcity of Indonesian data with other speech variabilities. To develop Indonesian automatic speech recognition (ASR), we present our research on state-of-the-art speech recognition models, namely Massively Multilingual Speech (MMS) and Whisper, as well as compiling a dataset comprising Indonesian speech with variabilities to facilitate our study. We further investigate the models' predictive ability to transcribe Indonesian speech data across different variability groups. The best results were achieved by the Whisper fine-tuned model across datasets with various characteristics, as indicated by the decrease in word error rate (WER) and character error rate (CER). Moreover, we found that speaking style variability affected model performance the most.