If you want to fully pay your monthly balance immediately, go with the ones that offer what you want to have (air miles, cash back, etc).
Target redcard gives 10% off for one day shopping everytime you get 1000 points (meaning you've spent $1,000). Amex gives 5% cash back for dining, although some places don't accept Amex. Discover also offers good cash back but some places (like Kentucky Fried Chicken, for example) don't accept Discover. Master and Visa give about 2% cash back and they are more widely acceptable.
There was an article couple of weeks ago regarding the "premium perks" like Mileage, etc - that the credit card companies will charge annual fee for those perks.