If you do not have a credit history the best thing to do is to start with a "Secured" credit card, they will ask you for a deposit and you borrow against your own money. Only use 25% of the credit limit and payoff balance as soon as you get the bill and continue to do the same. To get credit scores you do need to have 2 to 3 lines of credit reporting to the credit bureaus for at least 3 months. Lower scores mean higher rates, higher scores mean lower rate. You can always negotiate your rate with banks but with today's market, rates are not going to be pretty so you always need to focus on high credit scores.
If you already have 1 or items reporting to the credit bureaus then you want to make sure you have a low balance and payments on time for a minimum of 6 months before applying for an additional account as this will help you get a better rate and at this economy you really need to review and wait for the right moment.
You need to use your credit smartly and understand this can affect one day the rate on a car or home loan so do not just apply because you want a credit card, apply because you want to start a credit history that will benefit you in the future. Keep in mind that credit is something you need to work for and will benefit or affect you for a very long time.
I do recommend you talk to your parents if they are credit savvy and have a good credit history, ask them to add you as an authorize user to 2 of their credit cars (as long a s they have a low balance on these, if they do not then do not even consider as they will start you on the wrong track). Once you have 2 lines of credit for a minimum of 2 months you can apply for your own, by this time you have a chance to get a much lower rate.
American Express is a great card for someone that will really benefit from it and having the annual fee will not affect when you get all the perks and points otherwise it is not worth it. If what you are looking is for a card that offers good point system for future flights check this link or look for other options and see what works for you, everyone is different and we all have different spending habits so what is good for me may not be good for you and vice versa
Whatever you decide at the end, do your homework, just like when you were looking into applying for the academies see what they have to offer, put everything into perspective and see what is the best for YOU. This is the beginning of your credit history and this will stay for years in your record, you want to make sure you can get the best available for you.