Your questions fit perfectly into the purpose
of this forum.
As a long-time Java EE developer with 3 years of MongoDB under his
belt, I think your first idea is extremely doable and, in fact, I
wouldn't choose to do it any other way (I'd write it as a web
application using JSF or Wicket rather than a stand-alone for
maximum effectiveness, sharability, etc.).
As for the developer course, I'd concentrate on them separately.
You might do the Java one now and leave the DBA for later because
a) you don't need the power of replica sets, sharding, etc. that
you'll really learn in the DBA course while b) you'll learn more
than enough during the Java course to manage the database (you
don't have to wait for the DBA course to know what you're doing).
Cheers,
Russ Bateman