The datacenter's nameservers are likely only to be used for resolving names. I doubt they'll act as authoritative nameservers for the zones that you host. Send them an email and ask about it.
Set up your server as the master, then look for a service such as DollarDNS to act as the slave nameserver for all your zones. There are plenty of other places that do DNS hosting, but the guy that runs that one really knows his stuff, and will walk you through and explain everything you need to do, so you actually understand what's going on.
An interesting statement since I currently manage five internal linux servers and one windows server, which I have been managing for the past 2 years.
My problem is, I have all of around 5 months experience in the webserver field, and setting it all up on one IP has stumped me a little (first time iv'e had to do this, all other webservers iv'e ever had have had at least 4 ip's).