…. or are they all basically the same? Rather not pay!

Mostly the same, I use the free one from no-ip but most router providers have their own these days.

I’ve used dyndns for years, though by ‘used’ I mean ‘had kicking around for no good reason’.

BT seem to favour paid ones only 🙁

To do what, exactly?

To do what, exactly?

Give remote access to a router and/or a web server located at another property.
At the moment I can use Team Viewer to access a laptop there (logs and uploads Solar PV data) and then use its browser to access the router admin pages – but that’s a bit clunky! I may also set up a raspberry pi there to control a couple of zwave devices via a web interface.

I use noip.com, never had any problems with it, but I suspect they are all much of a muchness.

Give remote access to a router and/or a web server located at another property.

I use the free noip.com service to do this. I do also use a VPN though.