I also second Paint.NET - as a "starter". Very easy to use and if you erase a part of your image, it will automatically become transparent. There is a "magic wand tool" which lets you select colours like your white background. One click. Then press the Delete key and all is gone.
Under Window > Preferences > Applications, you can set your favourite image editor. Now if you right click on a face and go to Texture menu item, there is a possibility to edit the texture image. Do the deleting in Paint.NET and upon saving, it will automatically update the image in SU.
You really need something better than MS Paint.
[image: yDM0_transparent.png]