Echoing some others' opinions and adding a few new ones of my own:
THE MSc STRUCTURAL
1) For better or worse, the trend in the US seems to be that large, top tier firms are asking for Masters degrees with their rookie engineers. In this respect, it therefore makes sense to hit grad school before you hit the job market.
2) There is a very real chance that your master's degree may plant within you a bug for academia. If that's the case, then you'd be much better served by getting started with your graduate career earlier rather than later as academia definitely a young person's game with respect to career trajectory.
3) I feel that the timing of your masters degree is mostly unrelated to when you take your SE. The SE is a practical exam that should require no more academic knowledge than you should have gotten with your bachelors degree but a great deal more practical knowledge that you could only ever get on the job. In terms of theoretical material, I would expect and hope that your masters degree course content would be elevated well above anything that you would need for SE.
4) I started my course based masters seven years into my engineering career. I feel that the quality of my learning benefited enormously from that. Having a sense for how real engineers deal with real problems is a huge asset when it comes to approaching new academic information. That said, I could have achieved the same effect by just reading some good books and forgoing the masters altogether. It takes some serious discipline to do it autodidactically though, so the structured program is helpful there.
THE MBA
5) In my neck of the woods, there are dual stream programs where you can get and MSc and and MBA in three years. If I had it to do over again, I might have done that.
6) I would again do the MBA early on. I feel that folks often tend to think of this in the reverse order that they should. Usually people wait until they get a management opportunity and then get the MBA to bone up on the skills required for it. I feel that the reality is that, as a junior engineer, you need to demonstrate an aptitude for project management and entrepreneurship before you get the management gig. Otherwise you simply may not get it. So early on is when the knowledge and commitment to PM and entrepreneurship will really benefit you. Another thing to consider is that many MBA's subsequently decide that they would rather be business people than engineers. If that's the case, it will behoove you to figure that out early on.
7) In my opinion, a "Serious MBA" is someone who goes to one of only a handful of top tier business schools and goes there more for the social network that they will gain access to than the knowledge that they will acquire. These folks are headed to wall street and fortune 500 firms and would probably be disgusted to find themselves at the helm of a lowly, engineering consulting firm. As for the rest of us "non-serious MBA's", I'm not actually sure that the MBA is required. Much can be learned on the job and it's quite an easy thing to pick up most of the content of an MBA program from books. I've been doing that myself for a while now. You know, just truly the art of business administration as the letters of MBA would suggest. All this said, a non-elite MBA would still have value for:
a) Demonstrating to an employer that you are interested in and committed to entrepreneurship and;
b) Acquiring business administration knowledge in a structured way if self study isn't your game.