1) That depends on what your travel goals are. Do you want free airfare or free hotels? What is your home airport? Do you want to travel domestically, internationally, or maybe to Hawaii? Will you be travelling alone or with a companion? There is no one best card for everyone, it all depends on what meets your own personal needs. My two favorite all purpose cards are the SPG Amex (it can be redeemed for hotels or transferred to airlines such as Delta, American, and US Airways) and the Chase Sapphire Preferred card, which earns points transferable to United, British Airways, Korean Air, Hyatt, Marriott, Priority Club, and Amtrak. However I had my mother sign up for a Hilton Amex as she is not willing to pay an annual fee or cancel a card after a year, but at least she is earning something for her spending.

2) A mileage run is where someone books a flight, typically with lots of legs or long distances to earn miles and earn elite status. I've never been on a mileage run, and if you need to ask, you probably don't need to be doing them either.

3) I think the best tip is to earn points and miles free through signing up for credit card bonuses. If you read the travel blogs (try Boarding Area to start) you will read when special offers are available, such as small quantities of miles for signing up for something. I usually don't pay for points, how much you should pay for them depends on what value you expect to get out of them. If you are close to reaching a goal such as a free business class ticket to Europe or Asia, and you expect to get 3-4 cents per mile, then I might pay 1.5 cents per mile for them, but someone else might be willing to pay more for them. I do participate in E-rewards and E-miles which gives me small quantities of miles or points for participating in surveys. Now I'm using E-rewards to save up for a Hertz free car rental week in Europe, all without ever renting a car from them.