I had some crud on my sensor going back 8 or 9 months ago, I attempted to blow it away with a blower brush which had some kind of residue on it and accidently touched the sensor leaving it in worse shape. I took the camera to a specialised optics company and it cost $60 to have the sensor cleaned.
Now, last weekend, after shooting a full summer of motorsport, and getting covered in dirt at the latest drift round I decided to give my camera a clean. For the outside I used a 15mm wide soft-bristled paint brush my g/f picked up from Spotlight. Of course it was brand new and I cleaned it before using it. This works really well for the outside of the camera, getting into all the hard to get to places and around the viewfinder.
For the dust that had collected on the focus screen etc. inside the camera I used my Hurricane blower, any good quality blower brush (witht he brush removed) will work. Just be sure to give it a good few pumps to clear any dust out before aiming it at your camera.
The technique I use is to have the lens mount side of the camera down and blow up into the body, this increases the chance of the loosened dust falling back outside the body. Finally I put the mirror up and gave the sensor a light blow, it was spotless, but just as a peace-of-mind thing.
I wouldn't be too worried about blowing the dust back into the body as the 350D isn't weather sealed anyhow, so there is a fair chance of the dust making its own way in there anyhow.
While you're there don't forget to clean the lens mount and all the terminals with metho on a cotton bud.