Help for self host gaming server and some app

Hello everyone :D

I’m looking to host some gaming servers to play with my friends (minecraft, enshrouded, and others), and some apps (paperless-ng, jellyfin, seafile, etc.). Each game server must be accessible from the Internet, but only certain applications will be accessible (jellyfin, etc.)

I don't want to open any ports on my router or share my public IP. I already have a domain name, and I'm thinking of using some VPS to host a reverse proxy with tailscale or netbird.

For the VPS, I'm thinking of using OVH with unlimited bandwidth. I already have the domain name here, and I live in France where the servers are.

A few questions :

• Is this a good idea ? Any better solution is welcome.
• I don't really know how I'm going to redirect subdomains to use the correct reverse proxy. Local DNS on the VPS ?
• Tailscale or Netbird ? (I actually don't have any idea)
• Won't using Tailscale or Netbird like this cause performance losses on game servers ?

Reverse proxy :

• nginx for application
• infrared or gate for minecraft server
• Others for different game servers if needed.