I won't disagree with all the great advice of the previous posters, but I will add some of my own from my experiences with the mouse.
First 2 quick corrections from what I saw above:
1) Disney selects upper management 50/50 from internal and external. Obviously there are years when it is balanced one way or the other, but averaging it out, it's pretty close to an even split. This split however does not extend to corporate management (think Burbank offices) as over there it's closer to 60/40 in favor of external. That doesn't mean working your way up is bad. Just remember that you can always leave and come back. I think those were the most successful CMs that I met -- those that started at Disney, picked up other skills and experience outside, then returned at much higher roles.
2) All upper management have postgraduate degrees - False. I knew two park VPs who had only bachelors degrees (both in finance) upon ENTERING their roles as VPs. It seems as though the company is okay hiring upper level management without a postgraduate degree but they are expected to at least pick one up. On the other hand some had doctorates - e.g. Dr. Beth Stevens. The only reason I bring this up is that a common trouble in today's hiring market is overly qualified candidates. If you pick up a master's degree right out of college, a company knows that it does not represent as much about the individual as one who got the degree later. Also, if you speak to any MBA program they will tell you that much of the learning that goes on depends on the life/work experiences of the class members. If they all have minimal experience, the quality of your education suffers and it is reduced to just "book learning".
Now, onto more positive things:
Absolutely, 100% do the college program. It seems you're local, but CPs (although treated like slave labor) often get perks when it comes to flexibility of scheduling and being able to lobby to shadow different positions or meet people (remember: network, network, network). Additionally, although not necessarily recommended, the fast track to lower management is to participate in the CP, then directly apply for a management internship. The upside to this is that you could be a front line manager in under 2 years. The downside is that you are very green and your chances of being a good manager (barring exceptional natural talents) are slim. However, as long as you're not a bad manager there is a good chance you will stay in that level role.
As for degrees and direction, it may just be my perception, but it seems that Disney places higher than average value on hotel/hospitality experience. Much of this is probably due to their (fairly accurate) perception that all customer service is based on theories of hospitality and thus those skills are easily transferable to any part of their operation. Additionally, more than half of the WDW executives with whom I've been acquainted have been in hotel/resort management as some time or another before becoming Disney execs. With all that in mind, I'd say if you want to aim for the top, go the hotel route. There are fewer people competing for those management positions, but they tend to attract very talented personnel (not to say the operations managers aren't superb -- the most talented front line manager I ever met was a custodial manager).
Best of luck to you and just remember even if Disney doesn't work out at first, you can always come back to it. If you have any specific questions, feel free to PM me.