Take also power consumption in consideration. I myself have run a homeserver based on an older amd processor and recently updated to a low power device. The old server had a standby powerusage of about 60-70 watt. The new one has a standby usage closer to 2,5 - 5 watts while having a lot more performance. Depending where you are on the world and the powercosts the powersavings you have offset the costs of new hardware within 1,5-2 years if the server runs 24/7.

When and if you need a homeserver realy depends on your specific needs. For me: I do not want to use cloud services as primary storage for my personal and family photos. I want to run homeautomation based on homeassistant and a password manager on my own server.
For you it might be different. Consider that network storage from a fileserver has typically a lower performance so using it for games and gamefiles might not work.

Also the type of fileserver to deploy (windows shares/samba vs nfs) depends on what os you run on your laptop. Typically i would assume you use windows and would a linux server running samba be most logical choice. Or a more preconfigured os like openmediavault which helps a lot with a more intuitive gui.

However if file sharing is the only usecase maybe a nas like a synology, qnap or asustor might be a easier system to setup. This also tackles the powerconsumption issue.