Regarding the environment setups I would suggest you to look the docs : https://docs.railway.com/guides/environments

For the persistent storages you can mount directly for file uploads or local DB files or you can use external S3-compatible solutions like the pre-made MinIO template for easy object storage setup.

For optimizing build times and deployment speeds:
1. You can use Railpack or your own custom multistage docker file instead of default Nixpacks.
2. You can also arrange docker file layers smartly (e.g., copy only package.json before installing dependencies) so cache can be reused across builds.
3. Enable BuildKit caching(with mount cache ID) in Railpack builds—this speeds up repeated runs by reusing layers efficiently.

Few useful references :
https://railpack.com/guides/running-railpack-in-production/
https://docs.railway.com/guides/build-configuration

Regarding the environment setups I would suggest you to look the docs : https://docs.railway.com/guides/environments

For the persistent storages you can mount directly for file uploads or local DB files or you can use external S3-compatible solutions like the pre-made MinIO template for easy object storage setup.

For optimizing build times and deployment speeds:
1. You can use Railpack or your own custom multistage docker file instead of default Nixpacks.
2. You can also arrange docker file layers smartly (e.g., copy only package.json before installing dependencies) so cache can be reused across builds.
3. Enable BuildKit caching(with mount cache ID) in Railpack builds—this speeds up repeated runs by reusing layers efficiently.

Few useful references :
https://railpack.com/guides/running-railpack-in-production/
https://docs.railway.com/guides/build-configuration

What's the recommended way to manage environment variables for different deployment environments (e.g., development, staging, production) on Railway?

They have good documentation, what are you trying to achieve?
https://docs.railway.com/guides/variables#using-variables-in-your-services
https://docs.railway.com/guides/variables

How should I configure my project for persistent storage on Railway, especially if it requires file uploads or database files?

You have to use volumes https://docs.railway.com/guides/volumes

Are there any best practices for optimizing build times and deployment speed on Railway for a typical web application?

This one really just depends on what you are doing. Starting point use Railpack. If you are using JS use things like Turborepo.

They have a list of best practices that will help https://docs.railway.com/overview/best-practices