There is some very good advice on this thread, particularly in regards to public accounting. Based on my experience working at a then Big Six firm, some additional comments:
1 - Outside of IB or consulting, public accounting is one of the most lucrative careers for an undergraduate business major. Like someone upthread said, go with the biggest company you can get hired by. The Big Four should be your target. They may not pay much more out of school than other employers, but they offer the best networking opportunities.
2 - Undergraduate GPA is of significant importance to accounting companies. Firms will have hard minimum GPA’s to qualify for interviews, and that will vary based on the school, the season and the hiring demand. A firm that has a minimum GPA requirement of 3.4 for U Michigan might require a 3.6 from Michigan State or a 3.8 from Grand Valley State.
3 - GPA also matters after you have been hired. The better qualified new hires get typically assigned to partners with profitable practices in growing industries, while the less qualified new hires get assigned to non-growth industries. Since most new hires at end up working in the industry they specialize in, try to get into a growth industry.
4 - Once you start working, the school and GPA get tossed out the door, and future advancement is generally based on performance only. There is also is alot of turnover at public accounting firms. We expected new staff to stay with the company for three years max before they moved on. This is by design as many of the new staff that leave end up working for clients who then refer work back to the firm that first hired them.
5 - The most successful accountants have developed business skills outside of accounting. The CPA that makes partner or CFO has strong sales, management and people skills. I would push my kids to try and develop those as much as possible at a young age.
6 - Look for other professional designations like the CFA to boost your career. These are easier to earn when you are younger and fresh out of school than in middle age juggling a career and family.
7 - Use the 150 hour requirement to work on your masters. If you attended a lower ranked school, try to move to a higher ranked school for the post graduate degree. Admissions to a masters program is frequently easier than attending an undergraduate business program, and you significant increase your hire-ability by moving up a tier or two of school.