Amex just increased the publicly available welcome bonus on the Delta Gold SkyMiles Credit Cards to 50,000 miles and a $50 statement credit (OFFER EXPIRED), but if you are going to apply for the personal card you shouldn't apply for this offer.
There is currently a better offer available on the personal Amex Gold Delta SkyMiles Card is for 50,000 bonus miles and a $100 statement credit after making $2,000 in purchases within the first 3 months and making a Delta purchase (OFFER EXPIRED).
This offer is only worth $50 more, but you should be able to access it on Delta.com by making a dummy booking and you might as well take advantage of it.
If you are applying for the Amex Gold Delta SkyMiles Business Credit Card then the best offer available is the 50,000 miles and $50 statement credit since the higher offer does not show up on the business card via a dummy booking.
How To Get The Better 50,000 Miles + $100 Offer
The increased 50,000 mile plus $100 statement credit should be available to most people, but may not appear from some people depending on their IP address.
To get the offer you simply need to create a dummy booking on Delta.com.
First, you'll need to search for a flight (any flight seems to work).
You can select any flight option and click through the next page.
After selecting a flight and clicking through to the payment page you should see a banner featuring the 50,000 mile + $100 statement credit offer. If you use ad-block you may want to make sure this is turned off.