I's like to make more use of encrypted communication but, as usual, implementation across platforms may cause issues.
To this end I would like, perhaps, to purchase a public key and use a website secured by it to serve my keys.
Is that a solved problem?

Host your own keyserver?

https://keyserver.mattrude.com/guides/building-server/

Kind of depends. You could buy a cert or you might be able to make a self signed certificate that you carry with you on a flash drive.

Not totally sure what exactly you want to do with https but I assume you have your own server up.

I'd not considered that, tjhanks, might be worth a look.As it stands I have webspace on two domains but that is with a hosting service so I only have limited access. My thought process is that if I were to make one of them HTTPS then I could simply host my public key on that site and it would be relatively safe to assume that anybody picking it up had the correct key. Without HTTPS I envisage an automated main-in-the-middle attack could mean that the wrong key is given out. I'm not about to make myself a tinfoil hat but I'd like to be able to give my public key to people with a little assurance that it is my public key. It's the flash drive option I'm trying to replace for people I don't see face-to-face.

You would also have to use SSL certificate-based authentication options so that the server would check for a particular client-side key being presented. It can be done with Apache etc if you wish. ("https" cuts both ways ...)

Ah, yes, so if I give my public key out that's fine but I have no way of confirming the public keys others give me are genuine.
I'm beginning to wonder whether any of this is worth it. This is, in fact, one of the main reasons I don't use encrypted email on a dailey basis -- it's easier to assume all email is read and all is lies and to work around that.