You can get info on the Delta AmEx cards here. Note that the initial bonus for the platinum card is 15,000 miles, plus an additional 10,000 miles for spending at least $25,000 in a year. 5,000 of the 15,000 sign-up bonus (awarded only after the first use of the card) are base miles which count towards elite status. All 10,000 of the annual supplemental miles are base miles. It's all covered in the link and the following "Learn More" link.

The fee ($135) is pricey, but worth every penny. The cards are American Express cards, not VISA cards.

Also, although my card does have the annual companion ticket feature that akhullar mentions, it appears that this benefit is no longer offered to new card applicants.