1) The decision is obviously contingent on whether you want to stay technical, or move to management. I would say that the MS is going to precede or be concurrent with the MBA, but not come after the MBA. That's because after you get an MBA, you probably will never WANT to go back to doing purely technical work, especially if that MBA is from a top school.
2) Whenever you feel you are ready for a career transition. The decision should come naturally - it's basically whenever you can see that your career is decelerating and you feel that you are getting stuck in a rut. Some people never feel that and consequently have highly successful careers without ever getting an MBA (or any graduate degree at all). Keep in mind that not everybody 'needs' an MBA. You should get one only because you feel that you've reached a stage in your career where you're not getting as far as you would like and you think you need a boost.
3) This all depends on what sort of management you like to do. Some engineers simply want to move on to managing engineers or managing operations. Others see the MBA as an opportunity to make a radical leap to business functions that they have not been able to experience, i.e. marketing, finance, corporate strategy, etc. It all depends on whether you want to stay on the same path (but just move up) or whether you want to experience entirely new things.
I wouldn't say that any of these tracks are inherently 'better' than any of the others. The question is whether they are 'better' for you. Operations and technology management, for example, is a natural progression for most former engineers. It's comfortable, you will be able to hit the ground running. Finance jobs tend to pay very well and offer a lot of power and a direct shot to the CxO seat, but may present a steep learning curve to former engineers.
What's the value of an online M.B.A. program? I've seen a couple now that claim that the degree you will earn will not be an "Online MBA" degree, but instead the same M.B.A. that the students who attended the campus earn. The transcript/diploma will not differentiate between the two.
Far and away the biggest thing that you miss out on in the online programs is the face-to-face networking, which is arguably the most valuable part of any MBA program. The truth is, business success is often times not so much about what you know, but about WHO you know. It's hard to build rapport in a pure online setting. Fact is, much of the bonding of the B-school experience happens in the bars after classes, drinking beer with the other students. There's no such thing as 'Internet beer-drinking' (well, maybe there is, but it certainly wouldn't be the same thing).
The truth is, the MBA, just like any other degree, is an 'exploding' degree in the sense that 5-10 years after you get it, nobody is going to care that you have it. At that point, the only thing that people will care about is the quality of your work since the MBA. Hence, one of the only real 'takeaways' to any MBA program are the strong networking bonds you will hopefully have built.
Now, don't get me wrong. I think online is a great choice for those people who don't want to give up their jobs, and especially if your employer is willing to subsidize your tuition. In that case, you may not really need the networking that an MBA program can provide, because you will get plenty from just doing your daytime job. Of course, what would be even better is to have an employer fully sponsor you for an elite full-time MBA, but of course few employers are willing to do that nowadays (and justifiably so, as many employers will just take that MBA and then jump to some other company).