Does anyone know a (preferably self-hosted, but can be commercial) mail client that is as as good Gmail for power users? I always found it rather straightforward have a custom domain and even operate my own mail server, but haven't been able to do the same for the client.

The features most important to me are:

- Gmails speed and accuracy in search, especially on large mailboxes (100k+ emails) - this one is usually the deal breaker

- easy & powerful automatic filter rules

- web client

- calendar integration (optional)

- app for easy access to emails and search on mobile (optional)