Vanilla and small Paper servers
A small private server can often start with 2 to 4 GB of RAM. Paper or Purpur can improve performance, but plugins and view distance still affect usage.
Plugins and larger communities
Servers with many plugins, larger worlds or more concurrent players should normally start around 6 to 8 GB and be monitored during peak usage.
Modpacks need more headroom
Forge and Fabric modpacks can require substantially more memory. Check the pack recommendation and allow extra capacity for players and world generation.