Please note that a server is more defined by the intent, purpose, services, and operating system that the computer runs and not so much the type of hardware used to build the machine. That is to say that you can use enthusiast type hardware to build a server and that you can use workstation/server type hardware as a regular or gaming computer. You might want to think more about what you want to do with the computer and then decide if an all in one enthusiast gaming machine/server will meet your needs or if a dedicated media/file/mail/web/application server would be a better fit.
Not for nothing, if all you want to do is share files and media across a LAN but still be able to play games using that same machine, then build the gaming maching you would like to have and then purchase a hardware RAID controller card and some hard drives to store and serve out your media. If you plan on running Windows or Linux on all your machines, sharing files and media from the hardware RAID controller and a RAID5 array within your gaming machine is easy-peasy.