Seth Daniel’s Answer
I don't believe in "typical" career paths because we are all unique and carve out our careers based on what we're good at, and usually what we like the most. One of the fundamental choices you can make first is between research/analysis (often quantitative analysis and modeling are the entry level choices) and trading/arbitrage, or taking college classes across Finance and Math/Physics/Engineering that will prepare you for both. Once you are in a specialty in which you are skilled, you can move up (or laterally) within that specialty or expand into new areas or niches depending on your interests which will clarify for you on the job. For example, I worked with one colleague who thought she'd only be interested in equity investing, and but fell in love with fixed income trading.
One of the decisions you will need to make is whether you wish to push as far as you can technically, or whether you eventually want to be part of "running the enterprise". After about 3-5 years on the job, you'll be better able to make that decision if it's not readily apparent.
Others on this site may differ in their opinions, but I have vouched for starting at what you enjoy the most and for what you have the best developed skills. Be patient, learn from your mentors and colleagues, and you will find that both traditional and even very unexpected opportunities will present themselves if you perform on the job. There is a real danger in going into a career with pre-defined expectations. Once you obtain your first internship or job in investment management, do your best, and let the adventure unfold. It will be as unique as you are.