As a ME working in the racing/automotive industry I can tell you that experience is king in the engineering field. This becomes even more true when you are targeting a "small" industry (in this case Private space flight). Get into the best school you can, that as other people have said, gives you opportunities to work for professors doing research in the industry you want to work in. Unless you ABSOLUTELY can't leave home for whatever reason, follow the research.
Most importantly though, from your first day on campus start contacting the companies you want to work for and inquire if they have coop/intern programs. Getting a job out of school in a highly competitive industry such as the one you intend to work for is nearly impossible, but if you have previously worked for them you already have a foot in the door so to speak. Coop is usually preferable over interning because the company will have already invested lots of time in helping develop you as an engineer, and you will have made personal relationships with them.
Hope this helps and good luck.