Choosing the right hosting service for CPU-intensive Python applications, especially those involving data processing and machine learning (ML), requires careful consideration of various platforms, each with distinct features and limitations. Cerebrium is tailored for data-intensive workloads, offering a generous free tier with full feature access, pay-per-use pricing, and support from experienced engineers, though it may be overkill for simpler applications. Railway provides a modern deployment experience with a straightforward pricing model and useful free tier, but its ML support is basic, and resource limits can be surprising. Beam offers a Python-native serverless platform with simple deployment through decorators, but its free tier is limited, and it primarily supports serverless workloads. Render, while aiming for simplicity, imposes strict free tier limits and requires GitHub for deployment, which may be restrictive. Finally, PythonAnywhere is ideal for learning due to its simplicity but falls short for production environments due to severe resource restrictions. Ultimately, the choice depends on the specific needs of the application, and testing free tiers is recommended to ensure the platform aligns with project requirements.