Google is changing its Sites interface.
The “Classic Sites” interface allows for a lot more direct control. If you're used to old-school hard-coded HTML, you'd be more comfortable with Classic Sites. Many options which are possible (if hidden) in Classic Sites are just gone from New Sites.
But who knows how long Classic Sites will last? Google says it will give at least 1 year's notice before it forces Classic Sites users to switch to New Sites (but doesn't say a year from when).
(Of course this probably means that, if you only want your site to exist for a semester, Classic Sites is currently fine.)
The two are not interoperable - whatever you start a site on is what you have to keep using. There is not a migration path yet, though Google says they will create one when they force people to switch.
For these reasons, if you're just getting started, I think you're better off getting used to New Sites.