Maybe I haven't read it clearly enough. But where do you state what you want? Nobody can really tell you what you should do if you don't know yourself what you want. Getting a lawyer is pretty much the only reasonable response I've seen so far, because it can never hurt. But even then it is important that you know what you want, to find a good lawyer for your cause, and because a lawyer is a contractor himself and like you he would like to know what is customer wants before he can be really efficient. The second advice that always works is that you never deal with "The Big Corp" but with a guy or a team working in that big corp. While the corp might be reputable the guy might not be (and the other way around, though less likely). Learn to know these guys, not the corp. Both these tips (lawyer, learning to know people not roles/organisations) always works in every really important daily situation, not just start-ups, btw.
Do you want to get bought? Then start thinking about a fair price of your company. And start about an incredibly big number you would be happy to retire with. If you can find a result in between these numbers you will probably be doing not too badly. If you don't get close to either number, then you might change to the next goal.
Do you want to grow bigger to sell out bigger? Then look for a cooperation but keep your independence as much as possible. That includes keeping your company value secret (which is often more likely your market research than your source code).
Do you want to change the world? Well then try to find out what and how much they are willing to do. If they don't care about the cause, say "bye".
Do you just want to experiment, learn new stuff, keep your freedom? Then have a look about how much of that is left when they integrate you. You can't find out about this in a meeting room discussing with them, because they'll promise you anything in that regard. Look how the other people work in that corp. Are they creative, smart, free-loving animals, or are they cubicle workers who love to blame everything that happens around them on middle management? That's what you can expect after 1-2 years of integration.
Do you maybe actually hate the undefined future and hours of unlimited work of a start-up? This might be the best chance for you to get out. Getting integrated means you might end up in middle management with a decent pay and some savings from the sale in your bank account. That's way, way better than anybody can hope coming directly from university.
And one last tip, because I personally always struggled with knowing what I wanted when I was younger: Define a random goal. Choose one from them, maybe even using a dice. Doesn't matter. A bad specific goal can be changed when you finally know you hate it. A lot of unspecified goals get you nowhere.