Discussing which reverse proxy you should use is clearly beyond the supported area. 
But after looking at NGINX Proxy Manager for 12 seconds or more, I’d think that it’ll do fine. There’s another automagic NGINX proxy thing that I’ve seen discussed before as well, but with my extensive knowledge of NGINX Proxy Manager, I think it might be better. I might take a look at it, as I’m growing disenchanted with Traefik.
EDIT: Now I’ve looked at it for 3 minutes. I prefer tools that facilitate automation, so Traefik and https://hub.docker.com/r/jwilder/nginx-proxy (I found it) that allow you to add some labels or environment variables to the docker container so that no clicking in a web interface is required are more what I want, and it looks like to make that thing work you have to use the web interface or contrive to update the database manually with hosts that you want to add. But if you’re willing to poke and click on a web interface like a Normal Person (rather than a system administrator “person”), then it looks like that thing could be just what you’re looking for.