Presumably you collect Rapid Rewards when flying with Southwest. You could double dip, in a way, by paying for those flights with a card that offers Miles or Points when making purchases - and still collect Rapid Rewards for the flight itself.
DL belong to Skyteam. Have a look at the other airlines with which you could, if you went with Skymiles, use those Miles.. I think DL have recently cut back on the number of Skymiles given to pax for flights in some cabins / classes of service, and as such may not be as useful to you as other products.
Once the AA / US merger is completed, US will drop out of StarAlliance and join oneworld, which has BA in its fold. JetBlue don't belong to any one alliance.
You'll need to decide if you want to lean towards one alliance, or split loyalty between the three major players. You could obtain an airline-specific card, or consider something like an Amex, which will allow you to earn Points for use towards travel with a number of airlines.
It's really up to you which to choose; you'll have to consider the options and select a card or card that suits your needs. Some people are very alliance-loyal and others share the wealth (as it were) and work to maximise Miles accrual with one or two alliances.
You'll need to decide as well if your goal is simply to earn as many Miles or Points as you can or if you want to aim for status in an airline's program.
There is a fair amount of effort needed to make these decisions, but if you're going to use credit cards then ensure you get the most out of them.