When I was fresh out of college, I applied for an AMEX and Citibank Visa. AMEX accepted me and Citibank turned me down (no credit history).

I don't know why, but I held a grudge against Citibank for a long time.

I would start with the cards you think you might want and fill out one application at a time. If you get turned down the first time, then move on to your second choice, and so on. If you get turned down repeatedly, then you might need to get someone to co-sign or get it backed through your bank.

Filling out applications doesn't take too much time. Give it a try and see what happens.