Edit: thanks for the responses, I didn't know this was even possible.
I have a dynamic DNS thingamabob going (a script on a raspberry pi that pings my website a few times per day) and have had no problems. Haven't even noticed my home servers becoming unavailable due to IP address changes for a few years, probably because my ISP (Charter a.k.a. Spectrum) doesn't change my address very often. I use NearlyFreeSpeech for hosting the website and they also handle DNS and have an API for it, so it's all very nice and simple.
You can also use something like DuckDNS to have a backup in case you are away from home and your IP changes, you can still find your server. You could even theoretically write a script that then checks DuckDNS for your IP and updates the record with your Domain Registrar automatically (assuming they have an API)
More reliable than dyndns (since you never know how long DNS servers are actually caching)
Residential ISPs also often provide static DHCP leases that are quasi static IPs.
Some ISPs also sell an addon for a static IP to the service.