Drew, I am in the same boat as you only 10 years older. I've started a career (teaching) but have looked at changing. If you want inspiration look at the job shortage list here:
http://www.ukba.homeoffice.gov.uk/sitecontent/documents/workingintheuk/shortageoccupationlistnov11.pdfIf you're in one of the fields on this list it's easier for a uk employer to hire you according to the immigration laws. But as others have said this list changes all the time (at least once a year) so by the time you finish your degree the job might be off it. But I would make this list your first stop for considering careers then do your research. Why is this job I demand? What have been the hiring trends in this field? Is it likely to improve? (bad for you) Are there any incentives for uk citizens to enter this field (college scholarships, job placement agencies)? (also bad for you) Basically if the demand for a job looks like it will remain high and the people entering the field will be low, this is good news for you. That's why I considered chemical engineering because not everyone can cut the mustard in engineering.
My main advice though is to read as much as you can about uk immigration laws applicable to you. Know them well so that when things change you'll be ready to jump into action. (I even subscribe to the UKBA news RSS feed.)
The thing to remember is that you'll need qualifications that most UK/EU citizens won't have whether it's schooling or experience.
For example, I'm a high school English teacher so I'm looking into teaching at an American school in Europe or getting International Baccalaureate experience. These are niche jobs that not every teacher in Europe will have qualifications for. (BTW these ideas were suggested by the wonderful people on this forum!) I'm also not above getting citizenship in an EU country if I can get a job there. Because its infinitely easier for an EU citizen to move to the uk. But this plan might be nuts and will take many, many years!
Best of luck to you. It's hard for an American to move to the uk but I'm keeping the faith. If you do study in the uk look for a husband while you're there! I'm not suggesting you commit fraud. But true love AND the opportunity for a spousal visa is the best of all worlds.
This forum is a great help. Come back often!