I think you can combine both approaches - I think you should approach a university professor and ask them if you can "sponsor" a startup for class credit.

This has a couple benefits - you can churn out a basic prototype, and live "the journey" as you want. You can work hands-on, directly with top students, and go through the learning process with them. You can learn from them, they can learn from you - it'll be more relaxed that starting a company from the get-go.

This might also have practical advantages later on. If you decide to go for VC funding later on, you'll know both the software and hardware sides more intimately, and you may even get a higher valuation for having a legitimate product rather than a paper product.

You may even be able to talk the professor into letting you audit a few classes that you might need. Maybe you'll even take classes with the students helping you!

Perhaps consider outsourcing some of the fun? Say, self-study a bit, but also bring on a mechanical or electrical engineer to do the heavy lifting.

If you do go for a degree, I'd suggest electrical engineering. I know many great programmers whose degrees are EE, and it sounds like you'll need some expertise in that area as well. (No, I'm not referring to people from schools where CS technically falls under the EE department, like MIT -- though a joint program would probably work too).

I think bringing in more knowledgeable people in the future will be definitely necessary. What I'd like to do is to be able to build a rough alpha version (think Apple I), and then have people come and polish it (think Apple II). With more people and funding, we may be able to achieve Mac-level (relatively, of course).

My problem with the full EE course is that it will eventually require me to go into areas absolutely not necessary at all. But the same can be said for all other options as well.