An Internet connection is a no-brainer and they also recommend a headset with an in-built mic. APB releases on PC July 2nd, with 50 free hours.
Once the clock of free included times has finished ticking you'll need to either buy more hours, or cough up the usual monthly subscription fees. Here are the specs:
Core 2 Duo 2Ghz or equivalent 2GB RAM (3GB for Vista64 / Windows 7 64) nVidia GeForce 7800 - 256MB or equivalent 20GB Hard disk space
2GB RAM (3GB for Vista64 / Windows 7 64)
nVidia GeForce 7800 - 256MB or equivalent
20GB Hard disk space
Those are the minimum requirements to play the game, according. Sorry you can't keep that custom made content from the APB beta, recently, it'll all be wiped clean mainly down to compatibility issues - a clean slate for everyone.