As far as course study; you're getting into a lot of math, physics, and some computer programming. Any engineering degree will require calculus, physics, differential equations, mechanics (statics and dynamics), some sort of drafting/modeling classes, and some sort of intro to programming (matlab, C, etc). On top of that as an aerospace engineer I had a handful of courses in aerospace structures, propulsion theory/design, spacecraft design, aircraft design, fluid dynamics, modeling and simulation, vibrations, thermodynamics, gas dynamics, applied aerodynamics, labs, etc, etc.
Makes sure the school has an accredited engineering program (my company won't recognize you as a liaison engineer if you don't come from an accredited program) and preferably one with a Co-Op/internship program. The co-op will allow you to feel it out and makes sure you're doing what you want to be doing (and gives you some work experience.
In my current liaison position I work with electrical, mechanical, civil, and aerospace engineers. We've had a couple civil engineers come in who didn't know the difference between a rudder and a flap, but after a bit they ended up working just fine. As long as you know your engineering fundamentals you can adapt.
My group works assembly nonconformances. Essentially when something doesn't meet the engineering definition we either find a way to make it work, or throw it away. This could be anything from mislocated fastener holes, to large machinings that are damaged when a mill crashes. We have to make sure that the nonconforming part can still take the design loads (while maintaining a margin of safety) and perform the designed function. We spend a fair amount of time in the shop environment and work hand-in-hand with the guys who build the product to make sure that whatever repair we give to them can actually be accomplished (nothing like trying to get a rivet gun into a tight area). We get to be 'hands on' and work on all parts of the product (crew systems, flight controls, structures, landing gear, etc).
Since we work with all of the product we're kind-of a 'jack of all trades, master of none' type so we do a lot of coordination with experts in their relative fields (landing gear structures, or crew systems for example).
Production schedules usually keep things stressful, but theres nothing more rewarding than watching your work fly away.