I have finally taken the plunge and abandoned using Thunderbird as my mail client. Running four different e-mail accounts, Thunderbird made it easy to download all my mail to one place, as well as allowing me to easily move messages between accounts, while the Lightning add-in did a fair job of handling my calendar. Unfortunately, Thunderbird had taken to hanging for several seconds at a time while I was typing, and this seemed to be becoming more frequent. Also, synchronising the calendar with my mobile was far from satisfactory.
When I recently changed my mobile for an Android model, the fact that three of my accounts were on GMail made it suddenly much more sensible to go straight to mail.google.com to see my messages, rather than downloading them to my PC's hard drive via Thunderbird. The only drawback was GMail's limited ability to create folders to put old messages in. Then a colleague explained how there was a Labs feature to allow child folders, and suddenly my last objection vanished.
(Incidentally, the feature is called 'Nested Labels'. Why is this still experimental? It's virtually a 'Make Program Usable' option, and it's standard in any mail client I've ever used.)
The fourth e-mail account is the one I have with my ISP. Nobody knows the e-mail address except them, which means all I get is the monthly 'your bill is ready' message, and the odd bit of marketing. I'll still use Thunderbird to check on those occasionally. The most recent mail from them was to tell me that they liked me so much as a customer that they'd spontaneously upped my download speed to between 8 and 24 Mbits. I checked straight away: still 6 to 7. But it's nice they're thinking of me.