You say you have used credit karma to get your credit score, while I think that service is better for tracking credit changes, you should definitely get your official credit reports (which you can get free annually I believe) to make sure there are no errors (more common than you would think).

I would get the two AA cards (50k x2), Chase Sapphire(50k), and the US Airways card to start (easy 40 k and a good start for the Grand Slam).

In a couple months, I would get the United Explorer and the Freedom cards.

This could potentially get you 100k AA miles, 130k United miles, and 40k US Airways miles pre-Grand Slam. I think that would get you well on your way if you could get all these.