Too slow out the gate with this- the above posters have made a lot of these points while this was sitting in my drafts!
Caveat: it is hard to make categorical statements, b/c there are so many variations, but:
In general, engineering is nearly or completely a separate admissions track;
In general, the admissions standards are higher than average within a given college;
In general, it is easier to change out of engineering than change into it later.
BME v a different engineering is only a ‘disadvantage’ if you decide you want to do the other later- but you can always go back and get that qualification.
If you think you might want to move into an engineering field later, physics is your best bet for an undergrad course: there is the most overlap- much more than chem or even math.
You might also consider a [3+2 program](http://www.usnews.com/education/blogs/the-college-solution/2010/08/31/3-2-engineering-programs-at-liberal-arts-colleges), which is fairly common at good LACs: you do 3 years of regular undergrad then 2 years of engineering and you graduate with both. That might give you more time to see how your interests develop- and some fun as an undergrad to go with it 