My iPhone is my stereo system, using AirPlay (built into the OS) and an AirPort Express, and a Creative self-powered speaker system. Once I configured the AirPort Express, I then did not need my MacBook Air to be running. My speaker set has a nice subwoofer and multiple tweeters (wired). There are better brands, but I'm happy with the way mine fills the room with a nice fidelity range. It also responds well to EQ settings, but sounds perfectly nice at flat EQ (the subwoofer "woofs" pretty well).
As for seeing your iTunes library with your Mac not running, I'm afraid you're limited to what has been synced with your iPad (the iPad's library). If your entire library is on your iPad, then great.
A note about AirTunes. Once you turn it on in iTunes on your device, every sound your device makes will go to the speakers. Some apps directly support AirTunes, but it seems like my iPhone 4 just pipes everything to it - even game soundtracks and alert sounds.