A lot of people don't get approved quickly for the Sapphire Preferred.
I just started and did the same Top 4 (Both Citi AA, Barclays US, Sapphire Preferred). Now I'll sit tight until I meet these minimum spends and after 6 months (Jan, 2012), I'll go after whatever the big deal is then. The Sapphire Preferred is an awesome card for me since I spend a good amount eating out and it is 2:1 for each dollar spent at restaurants! I plan on making that my everyday card after these spends.