I love being an automotive engineer. Even worked for Nissan for a while. Would recommend it to anyone who has a passion for cars. It's very difficult to answer the posed question without writing a book. Simple ones 1st. You can do a search on salary of specific jobs, entry level automotive can range between 35~70K depending on location, skills, etc. My personal (read biased) opinion is a mechanical engineering degree, but electrical, aero, industrial, and others may fit the bill depending on what interests you. If you are seriously thinking about it, I would suggest contacting your local chapter of SAE (SAE.org), they are always willing to spur young minds in the right direction (even if you are in high school). I've known automotive engineers from universities all over the US, Germany, England, Japan, etc. (the list really does go on). There are lots of really good engineering schools, some are better than other in specific fields. Once you get a good education & your 1st job, the name of the school becomes less important.
One thing most people don't understand is how a vehicle is conceptualized, designed, developed and manufactured. Thousands of companies are involved in the start to end result of manufacturing a vehicle. An engineer could spend his/her entire carreer designing one specific type of part (say oil filters or spark plugs), or they could end up in product planning trying to figure out market trends and what niche there new vehicle will fit in and what the customer wants. You need to experience vehicles and find out what motivates you. Student chapter of SAE does several design competitons (FSAE - is awsome) which gives students hands on experience to figure this out. I have a passion for handling rather than fast in a straight line, pushing cars through corners at the limit, so I ended up in vehicle dynamics rather than Powertrain, HVAC or IP design. I would say, regardless of the engineering discipline, computer skills are a must. Alot of engineers are mindless number crunching geeks, but there are real good engineers who communicate well, have good people skill and are creative. Alot of engineering is applied math, but it's more about the logical process that gets you there, and lots of problem solving. Driving 3/4million dollar cars around closed circuits at 150mph isn't the norm for an engineer, but it does happen for some of us lucky ones. Bottom line, experience as much as you can (electronics, design, IC engines, HVAC, NVH, whatever). Figure out what you are good at and enjoy.
Good luck to all