Here is my guess of what we will see happen.
Continental Airlines credit cards will become a thing of the past either later this year or the beginning of next year. If you want to add to your United account, apply for Continental cards before they’re gone. I would start with the Chase Sapphire℠ Preferred Card as they have the largest sign-up bonus at present: 50,000 points. They convert one to one into Continental miles.
My next application will depend on who puts out the next big bonus, either an American Express(R) Premier Rewards Gold Card , The Platinum Card® from American Express, or a new larger, improved bonus on the Continental Airlines OnePass® Plus Card. The current bonuses are 15K on the Premier Rewards card and 30K on the Continental card from Chase. For now, get the Sapphire Preferred card and wait it out a month or two for the other cards to increase their bonuses. I can feel it in the air. Any Continental miles Chase has purchased in advance won’t be much good to Chase when the merger is complete. I’m guessing they are still sitting on a boatload of CO miles.
And after these two applications, you still have the United Mileage Plus® Visa Signature® Card card to obtain. As evidence of the increasing bonus offers, I just got a targeted offer as a United MP Elite for 50,000 frequent flier miles. First time cardholders only, though. 
At the present bonus levels you will accumulate 50K+15K+30K+30K=125,000 miles in one program. That sounds like a first class ticket to me.
And the service from Chase is really improving all around. The Sapphire Preferred card gives 25% more on travel redemptions and a 7% annual bonus. I love talking to a real human being on the phone and I saved quite a bit since I encountered no foreign transaction fees while we’re traveling in Europe. And I have also noted an improvement in the responsiveness from the Chase secure email center as well. They really have taken over the credit card market while Citi seems to be very tentative in attracting new customers.
In short, get the Continental cards first, or the ones that transfer into Continental miles first. Remember that the transfer from Amex Membership Rewards to Continental miles ends on September 30th. That should be incentive enough to have you do cards that earn or can be converted to CO miles first. Remember the combined airline will be the largest in the world. You might as well have a few miles and future miles-earning credit cards with the biggest there is.
