Well, I'm a network administrator, and have been doing it for nearly 10 years..
I'm not sure what kind of IT related degrees are available in the US now, but I'm not aware of anything which is very relevant to network admin work, most are comp. science degrees I thought, which isn't really that useful if your aim is network administration. But any IT related qualification will be a plus. Ultimately hands-on experience is what will make the difference.
Which reminds me - when you say network admin, do you mean 'network' administration or system (server) administration. Some places consider them the same thing, but they can be very different. A true network admin is able to setup and manage large LAN and WAN environments, and generally doesn't bother with actual server management. A system admin is the reverse. Although, in smaller organisations you can be both (like me..)
So that will decide to some extent what you should study - network infrastructure like routers, switches, structured cabling etc, monitoring systems etc or admin/management of Unix or Windows servers.
Certificates are nice, but these are usually pretty easy to obtain "on the job" if your day to day work is relevant to the certificate.
Since it sounds like you are going into this fairly cold, some sort of college course is probably best. Personally, when I've interviewed people I've cared less about the fancy name of their qualification, and more about the content of what they've studied/experienced. But that's just me. Your mileage may vary, as always..
Graham