Comparing the Canon 90-300 to a 60mm Tasco isn't really fair. The 90-300 is a budget lens but not necessarily a crap lens, and it wasn't designed for astrophotography. If you look carefully at reviews, nothings perfect, not even the revered L series Canon Lenses and often simply stopping the lens down and not operating close to the maximum and minimum focal lengths will improve the results dramatically....
Trevor, probably the best way to improve your image(s) is to make sure the camera is accurately focussed, on a (sturdy) tripod and, if you can, use mirror lockup so that mirror vibrations don't affect the image. Stop the lens down to the smallest aperture you can manage (f8 or F11 taking in to account star trailing and sensor noise) and take several (bracketed) exposures. Also don't be afraid to up the ISO setting as the Canon sensor is a lot less noisy than other brands. On the 20D Long exposure noise reduction on will automatically take a dark frame and subtract from the image; I presume the same applies to the 350D. Processing with photoshop and registax as Paul suggests will also enhance the image and bring out more detail.