Why I use Fastmail.com

Same. I wish there were a plan that allowed use of a custom domain but had less space.

Is there a way to migrate a grandfathered apps email to this but still use the account to access Google services like the Play store?

I chosed Zoho mail over Fastmail, but not sure if this was good idea. Webmail is so 90s, and spam control is too agressive at Zoho. Will try today new Fastmail webmail.

Are there any neat things I can do with the web site functionality? Or is it static HTML only?

Big fan of Fastmail and have been a customer for ten years now, with no complaints. An example of the cool team behind it, too: I once hacked up a Perl script that would access my Fastmail addressbook over their LDAP interface. It was giving me trouble, and when I submitted a help ticket the guy who answered me actually fixed the Perl on my behalf. (Not linking to the code anymore since it's out of date, but I remember thinking, that is some awesome customer service). Other pluses: limited file storage you can access over webdav, a good history of communication with the customer including interesting blog posts, family accounts that allow you to share contacts and messages, and standards-client IMAP that means you don't need a special app to read their mail; any IMAP client will do. This article got the big picture right (you're the customer, not the target, etc.) but could have been more detailed in what's provided when you are a customer.

By the way, I know they're rolling out carddav and caldav systems for calendar and contacts, but in the meantime, the perfect partner for Fastmail in my opinion has been Fruux, which offers caldav/carddav contacts and calendar that syncs across any device, with similar customer service. I'm happy to pay for both because it means I'm not tied to any particular company, even if they back the hardware (Google/Android, Apple/iOS). Independence is worth the money, in my opinion and experience.