so you want the music not to play when the computer wakes up? And then push a button for it to start? This was a "feature" to make it play. Have you poked around WinAmp's settings? I haven't doen this because I want my music playing when it comes alive, so this is just a suggestion not a foolproof solution.
Also for the hiccups it is normal. That happens to music even if you play them in WMP on a regular computer, put it in standby, and resume. A little choppy at first. I think it has something to do with windows using all the resources to get itself ready again.