I'll start by saying that I'm not a SysAdmin (System Administrator), but I too am looking to get into the same line of work and have done my homework on the matter.
As for your question, certs don't make the admin. They are always a help in landing the job, but they don't by any means make or break your knowledge or skill levels. Network/Systems Administration is a job that you learn by doing, so experience is king. Most admins work their way up, and some might not even have any certs. Many are self-taught, but hold a degree. (it's not terribly uncommon to hold a degree that hasn't much to do with your job). Education is the second best, and is the acting-king when you don't have much (if any) professional experience.
An Associates degree is usually enough to land you an entry-level position, but it depends a lot on the position. While one might ask for nothing more than a basic knowledge of computers and Windows, another similarly titled position might ask for HP ProCurve and Cisco Voice experience, as well as MS SQL 2005 knowlege (IE, some get very specific).
If you start looking through job listings for the positions you want. Some will demand experience in things you can't get experience in unless you've work with it at a previous position (Blackberry Enterprise, HP-UX, Jupiter or Nortel network equipment, etc).
Your college experience will speak to any future employer much more than a cert. However, certs can't hurt. While your education speaks volumes about you, certs are merely a knowledge yardstick of what you know in a certain subject. If you have a Network+ for example, your employer will know that you've got a basic understanding of how a network works, common protocols and layouts, standard network hardware, and basic trouble-shooting at the very least.
Good certs starting certs would be the CompTIA Network+, Cisco's CCNA, as well as various Microsoft certs like those for Windows XP (70-270) and Windows server 2k3 (70-290). This also depends on what platform you prefer working with. While most places you go will have a mix of Windows and *NIX servers, many jobs at least want someone with that's familiar with Linux. In case my username didn't give it away, I've already made my choice.
HP and IBM are both in the UNIX game and have certs, but as a rookie, I doubt you'll land a job working with AIX 5L or HP-UX 11/11i. Certs for those are for the guys who've been in the game a while and have usually been working with it a while. Sun Microsystems and Red Hat both offer System Administration and Network Administration certs with their respective OSs.
Hopefully I've helped more than confused. If you have any more questions, just ask.