public (static) IP - more simple, less to go wrong
Depends on what you want it for. Dyndns is fine for my home machine. But I'd insist on static IPs for any school servers I had to directly put on the net.
Static IP, more than one, please.
I know, I'm eating valuable address space, but they are useful, damnit!
You usually need to give a reason to get >1 IP, but "I like numbers" appears to be valid for anything up to 16 ;)
Likewise, as good as services like no-ip.com are for pet projects, personal websites which might move about or just being able to RDP into your machine at home I insist on a a static IP for any commercial level project which obviously includes school. I don't think I've ever used as many as 16 but keeping mail on a different IP to your site hosting and remote access is defintely a boon for admin, fault diagnosis and to a certian extent security. Obviously an alternate IP wont stop a deliberate attempt to circumvent securty but I have found that having the mail server seperate to the web one saves on nusance traffic.