Gee, "network/systems admin/database administration/security" not only covers a lot of territory, it also embraces lots of certifications as well. On the systems admin/network side, pick a cert that matches the platform (Windows, Unix/Linux, Macintosh, etc.) that you work with most day-to-day.
Same for the database stuff as well. As for security, starting with CompTIA Security+, then chasing down a CISSP, CISM, or similar credential should help you decide what vendor-specific infosec certs should be helpful or necessary.
Sorry to be so vague, but I don't have the time or energy to lay out all the choices in each of the three or four major content areas in which you profess interest. My guess is that as you go a bit further down the path, you'll end up focusing your efforts within one or perhaps two of these areas, as the time, work and expense involved in getting certified makes itself clear to you.
This was first published in August 2004