Pretty sure there's no right way to do street photography. Even if there was I'd have to do the opposite anyways.
For a little while now I've been experimenting with what I call 'shooting from the hip.' With this the camera is hanging from the neck strap rather than at my hip but still just as unaimed. Snapping shots as I go, it's a bit of a crapshoot what I end up with. Still, it's lots of fun.
Ever since I started snapping photos with my old 110 I've had an aversion to posed photos. There's just something about the way people change in demeanor and presentation when they realize a camera is pointed at them that strikes me as unnatural. No offense to posed photos, I'm just not looking for people's 'best' side.
Lots of times I'll use a zoom lens so that I can blend into the background and still get shots but with a wide angle that's not possible. On the flip side, a wide angle lets you get all of a person in the frame even with it hanging from your neck. Gives it an odd perspective though. Still, with it hanging from your neck nobody realizes you're shooting them until they're close enough to hear the shutter and by then it's too late.
@scubahead made me think of the documentary Everybody Street yesterday so now I have to mention it. When I got started with photography I wanted nothing to do with street photography. Working in bars and restaurants will do a number on your fondness for people. Quite by accident I wound up watching Everybody Street, which is about NYC street photographers and it really piqued my interest and made me want to give it a try.
I periodically watch it again, it's good for a fresh jolt of enthusiasm for shooting people. Finished it up again this morning and had to edit some street shots, which is why you're looking at these from my recent trip to Washington DC.