Yes they'll help pay off debt, but not so sure about it in the Officer side of the business.
For instance, I'm training in ROTC right now (Army), and of everything I've read, heard, or learned from the Army, is that there seems to be no true school debt plan for Commissioned Officers.
However, Enlisting seems to all but guarantee those sorts of bonuses. Maybe it's just because of the ROTC route.
If you already have your degree, then I think how they go about it is like this:
You Enlist, and in your contract it is stated that upon graduating basic, and maybe after AIT (advanced training for specialty), you'll then ship off to OCS. You almost always have to have a degree to enter OCS, but as far as I can tell, you cannot simply go right to OCS without anything prior. So in this case, you technically Enlist, and I believe you are then eligible for all Enlistment bonuses, such as the signing bonus, and then the school debt bonus.
I am curious though, you seem to state specifically O2/O3. Have you talked with a recruiter? Is there a certain field you are specifically planning on entering due to your schooling experience?
Immediately after Commissioning, you'd be an O1, although you'd have to be a serious screw up not to get O2 within your stipulated contract time.
Between Army and Navy... well my gut says Army. But that's me. I have my reasons, and I also have my restrictions. No flying for me, which was my original dream. Color blindness makes the Navy scared, so much so that it's an immediate disqualification from any flight capability with no hope of turning that around.
But it all depends on what you want to do, and any personal beliefs/reservations. Many of the same job types are offered in all of the services. So it's mostly personal preference. Want to dodge the chance of being in a war zone? Sign with the Navy for a Naval-base job duty, or attached to a sea vessel. Just about everything else is game to be in a warzone these days. Naval warfare seems to be dwindling, not that there aren't other duties that are hazardous (pirates, random events, World War III, etc etc).
So... what is it you want? 🙂