I have listed items with references which will help you in deploying your ASP.NET Core site from scratch in a fresh VM for a production environment.

• Install and Setup Supervisor - It is a tool which will help in the auto-start of your site on server restart, otherwise, on server restart, you might need to manually start site.
• Install and Setup Nginx - For Reverse Proxying to your .NET app
• Install DotNet Core  https://dotnet.microsoft.com/download/linux-package-manager/ubuntu16-04/sdk-current
• Get a domain - Can get from GoDaddy or any other vendor.
• Setup and Install Lets Encrypt - To Obtain Free SSL Certification or if you have own certificate purchased you can also use it.
• Enable Firewall to allow port 80, 443 - or any other port based on your requirement.
• Enable https redirect in your Ngnix Configuration
• After Hosting ensure you have enabled basic Security Headers for the site - Can test Using Security Headers site- https://securityheaders.com/
• Can test your site for SEO if your site needs it - https://sharetechlinks.com/post/detail/101/free-seo-checker

References

• Server Setup
  You can get a cheap Digital Ocean Server for $5–$10 which is more than enough to run a simple site. 
  This site runs on same - https://sharetechlinks.com

• Enabling Remote Desktop - XRDP
  https://websiteforstudents.com/connect-to-ubuntu-16-04-17-10-18-04-desktop-via-remote-desktop-connection-rdp-with-xrdp/

• Installing Ubuntu Mate OS
  Usually, when you purchase Linux VM from Digital Ocean or any other Vendor you won't get OS. To install a lightweight Ubuntu Mate Linux OS

https://jerrygamblin.com/2016/10/19/ubuntu-remote-desktop-on-digital-ocean/

• Supervisor, Nginx Configuration
  https://www.hanselman.com/blog/PublishingAnASPNETCoreWebsiteToACheapLinuxVMHost.aspx

• Microsoft Official Docs
  https://docs.microsoft.com/en-us/aspnet/core/host-and-deploy/linux-nginx?view=aspnetcore-2.1&tabs=aspnetcore2x

• Nginx - In-Depth configurations
  https://sharetechlinks.com/post/detail/173/nginx-everything-about-proxy-pass
  https://sharetechlinks.com/post/detail/204/nginx-with-modsecurity-and-brotli-production-setup-dockerized

• Setting up Firewall
  https://www.digitalocean.com/community/tutorials/how-to-set-up-a-firewall-with-ufw-on-ubuntu-14-04

• Installing Putty in Windows

https://medium.com/@bharatdwarkani/5-easy-steps-to-install-putty-and-connecting-to-linux-ubuntu-server-in-windows-adcdc9d755dc

• Transferring file from windows to Linux using Putty
  https://medium.com/@bharatdwarkani/copying-a-file-from-windows-to-linux-through-ssh-17f4f4c2eca8

• Security Headers
  https://sharetechlinks.com/post/detail/133/adding-http-headers-to-improve-security-in-an-asp-net-core-application

• Refer this for Unzip file in Ubuntu
  https://www.hostingadvice.com/how-to/unzip-file-linuxubuntu/

• Installing My SQL In Linux
  https://www.digitalocean.com/community/tutorials/how-to-install-mysql-on-ubuntu-16-04

https://www.digitalocean.com/community/tutorials/how-to-secure-mysql-and-mariadb-databases-in-a-linux-vps

https://www.configserverfirewall.com/ubuntu-linux/enable-mysql-remote-access-ubuntu/

Conclusion
The above-mentioned checklist is more than enough to host your ASP.NET Core site in a fresh Linux VM starting from Scratch.