This probably will not be terribly helpful, I'm afraid, but I always use Photoshop for that kind of thing, it's awesome. Unfortunately, it is also pretty expensive, so if that is all you're looking to use it for, probably not a worthy investment. I'm not sure what other programs you can use for that type of work, all my experience is in Photoshop. It has a tool (magic wand) that will "cling" to the edges of an image, making it really easy to select one object, especially if it is set on a plain background. Then it has "layers" to work with, so you can put that object on a new layer of it's own, delete the background layer, and put whatever you want behind it. Then add any drop shadows, text, etc, and keep them all on separate layers so that you can easily change just what you need to.
I have heard good things about Corel Draw, but I don't know specifically if it does that. I actually picked up a copy that I got off Freecycle, but I haven't tried it out yet. I hope maybe someone else will have other software suggestions for you.