I master's degree is the new bachelor's.
I've read an MBA is often accepted as one of the most useful master's degrees as well (although I'm at the tail end of my MPS program). The nice thing about an MBA, as I have been told, is it leave many doors open. Traders, bankers, CPA, business owners.... know economics and business.
Once you have a master's degree an employers couldn't really care less about your undergrad education. For certain positions your expected to have, at a minimum, a master's degree.
Again, because I don't have an MBA, I can't speak to exactly what is available once you're done serving, but I can say a few things, from my experience....based on what I've been told and what I've seen.
The private sector loves ex-military, you'll get a job in no time.
I haven't experience that love for veterans. In fact, I would even suggest there is a great deal of misunderstanding from the private sector. I wouldn't say doors have closed for me, but it certainly didn't achieve the warm and fuzzies those still serving say it will. Sorry. On top of that, many things you do in the military won't translate. Then there's the public sector (govt). I know Obama is cramming it down your throat that government jobs are just WAITING for vets. They aren't. There will be a major influx of 10 point veterans (and if you don't have 30% disability, you'll just be another 5-pointer).
I appreciated the HBO show Veep, and the line "You gotta network to get work." It's true. USA Jobs is a general black hole for applications. Contacting someone or knowing someone in the office you're applying for gives you a flashlight.
You have a security clearance? They'll pick you up in a second.
If you don't have TS-SCI.... I don't see this happeneing. I've had TS for...a while, it might get you a second look, but you know what? MANY people have secret, and a good number have top secret.
Government contractors love ex-military.
That's probably true. After I left the Coast Guard I spent 6 months looking for jobs. The first couple of months I looked in the private sector; things like nonprofits and corporations. At some point I applied to Booz Allen Hamilton. The next morning, I got a call to set up an interview. Booz Allen has a "speed dating" kind of interview process, which I actually liked (and after a number of interviews at other places that didn't go anywhere, I think I was a little more "myself" for this interview). I interviewed on a Wednesday, got a call on a Friday which sounded suspiciously like an offer, but it went no where.
Eventually... 6 months down the road, Booz Allen did give me an offer, but I had already started at a small PR firm and felt like I should stick it out with the firm (despite a better paycheck from Booz).
I'm guessing contractors do like military, and they would generally put you on a contract with an area you're somewhat familiar with. It's hit or miss. You client may be great, or may be a train wreck.
Also, contractors feel the budget squeeze too.
(Side note: while the process with Booz is horrible, I've heard people generally like working there, and the benefits are good.)
Your undergrad program is important with respect to.... does it limit your graduate program options.
I was a government major at CGA. That choice did not limit my application and acceptance to the strategic public relations master's program at GW. I have a feeling if I was applying to an advanced civil engineering master's program, I would be limited.
Choosing management will not limit you from an MBA. Just make sure you do well, because your undergrad GPA can come back to bite you (how mine didn't I will never know).
The sky is the limit though. Sometimes you'll have 15 interviews and no news. You'll feel down and sad/angry... and then things happen and you're "back on top". I left the Coast Guard in 2011. I spent 6 months looking for a job. I took one at a small PR firm. A month into the job I got an offer from Booz Allen. Five months into the job (on a miserable DHS contract), I decided to look elsewhere. Somehow, as I really figured out how unhappy I was, two other PR firms reached out to me, I contacted Booz Allen again and finally a professor I had recruited me for a position at a financial regulatory body in DC (which I took) and I've been very happy since.