Here is a good article for setting up a reasonable production environment on a cloud linux virtual server. I use something similar, except my deployment is via git.
PLEASE DON’T RUN rails server ... outside your local development environment
I currently have 3 Rails projects running on my vServer. The solution may not be the best, but it works for now with domain.tld:3001 until domain.tld:3003
A easier solution to deploy multiple rails app on the same virtual server is to use Dokku, The installation for Dokku is straight forward and it allows you to have your own person heroku like paas. I’ve been using it for RubyOnRemote on a $6 Vultr VM without any issues. You can also leverage BuildPacks from Heroku if you need to customize your setup.
Using Dokku removes a lot of work for infra management and lets you focus on writing your apps instead of figuring out how to run them.