If it’s only you (or your household) that is accessing the services then something like hosting a tailscale VPN is a relatively user friendly and safe way to set-up remote access.
If not, then you’d probably want to either use the aforementioned Cloudflare tunnels, or set up a reverse proxy container (nginx proxy manager is quite nice for this as it also handles certs and stuff for you). Then port forward ports 80 and 443 to the server (or container if you give it a separate IP). This can be done in your router.
In terms of domain set-up. I’ve always found subdomains (homeassistant.domain.com) to be way less of a hassle compared to directories (domain.com/homeassistant) since the latter may need additional config on the application end.
Get a cheap domain at like Cloudflare and use CNAME records that point domain.com and *.domain.com to your dyndns host. Iirc there’s also some routers/containers that can do ddns with Cloudflare directly, so that might be worth a quick check too.
I’ve borrowed a top spec Audi A6 from 2004 for a bit last year and that had adaptive cruise control as well. Honestly if not for the infotainment GUI, which felt very “spy kids”, it would have passed for a ~2020 car as well feature wise.