It’s been a while since I had the need for a fixed IP but it would be handy for a project I’m involved in. What’s the current cool way to get one (getting one from our ISP is not possible). Free would be good, cheap is acceptable 
Edit: should’ve added that it will be a self-hosted thing sat in front of a large amount of storage, incase that’s a consideration.
Dyndns?
Was just checking them out. It took me a while to remember who I had one with. It was quite a while ago and my memory isn’t what it used to be 
It is a while since I used them, but always worked fine, IIRC for the free account every month you have to confirm via email link still active if no traffic.
this sucks.
it’s 50/50 whether dyndns will work for you.
when i had dynamic IP, certain services just did not work due to ISP’s routing settings.
for instance, i got working SSH only when i got static IP.
so it also depends what ports are you going to use.
Yeah. We’re in quite a rural (very!) place and isp choices are very limited. The one (best) we use want a small fortune for a fixed IP. Not really worth it as the project is already going to cost me money (and time!) 
I tried determing our current IP address and setting up port forwarding to an internal web server but the request gets denied. I guess the ISP has something in place to prevent that? I can ping the IP though so it definitely responds. I guess without that DynDNS (or similar - Dynu?) won’t work anyway?
i’m lucky since i live in Ukraine.
we have one of the best internet tariffs in the world, and static IP costs me less than €2/month.
looks like usage of ports below 1024 is restricted somewhere on ISP side.
this is pretty typical situation.
Damn! I think our ISP want €2 a second! 
I would guess that these days most home ISP’s will not do this for you. IPv4 space is becoming limited. I would guess your best bet is with a webhost that can give you an IP - your project would need to be hosted on their servers as well. (disclaimer: I work in this industry).
many of us do 
was just looking into this the other day for a media center I am setting up behind vpn
if your isp don’t offer it, some vpn services like nordvpn offer static IP
it’s not cheap though
How often does your IP change? Mine hasn’t changed in 3 years. Just a thought.
Edit: I stopped getting them for clients as well since the work from home move. No problems.
How about this:
That’s a good point but I was trying to get around the fact that it seems our ISP blocks incoming traffic on our public-facing IP. Is that a thing and is that a thing that can be gotten around?
That’s some good thinking but surely I’d still need a static IP to route the VPS to seeing as all the files I need external access to are sat on a drive connected to a raspberry pi on our local network.
Yes, some ISPs are blocking traffic on low ports (<1024) and, no, there is no way around. So in the end it depends if you really need these ports or if you can use different ones (for example: you can reconfigure SSH to use a different port).
If this is just a service for limited use, not for the general public, then using alternative ports shouldn’t be a problem. For example, putting the web server on port 8080 is pretty common, and sshd could use something like 2222.
Hmmm. Tried changing both the SSH and webserver ports but still the inbound connection is refused.
I’ll keep digging.
Is there a firewall running? A decent OS will have a firewall that blocks most incoming ports by default.
Yep, as @PofM already mentioned, check for firewalls. Especially check the one on your internet gateway (router/cable modem). Some filtering may already happen there …