1. Accurate, deterministic, fast search of your email
2. Whatever they call the categorized inbox, I use "Primary," "Promotions," and "Updates."
3. Labels implemented as labels, not mapped clumsily onto the "Folder" concept.
If I were told I had to not use the Gmail UI, I would 100% switch to another email provider immediately, as using Gmail the service with a vanilla IMAP client is way worse than just using a normal email host with the same.