Assuming it's a web server, then expense is not necessarily an issue. An old Pentium-100 can do the job; the more memory and hard drive space the better. Install a bare, efficient Linux distribution with no desktop etc, and add Appache. Hey presto, one competent fast world-class web server.
I was running an old Linux server on something like an AMD K2-450 for years until the fan failed and a hard drive died. That provided web, file and print, time and database service effortlessly.