I don't think prestige of one's undergrad is very important at all. I'm sure the schools consider the school you attended, but from people I've talked to, it seems to make little difference if any. If anything, I would think the law school admissions officers might adjust one's GPA based on how competetive the undergrad school was. Alternativly, they might look at class rank instead of GPA (ie, consider the top 30% of an Ivy to be comparable to the top 20% of a second tier undergrad.) My guess though is that law schools aren't as reputation concious as the applicants.
As for your major, I don't think the school gives much weight to one's major other than to consider (1) the difficulty of the classes and/or (2) the diversity of the incoming class. They probably want multiple majors represented, and they probably allow a slightly lower GPA from those with very difficult majors (Bio-Chem or something like that.)
None of this is fact, or even well researched analysis, but this is the impression that I get. I'd look first at the LSAT / GPA numbers, decide how high to aim, and apply to a range of schools.