Alternative to Photoshop or Paint.NET

GIMP (install) should do the job.

Many people I know complained that GIMP has an awkward and unintuitive user interface, but hopefully you can get used to it and get the job done.

As others have said GIMP is an excellent graphics program. I personally have not had any problems with the interface - I find it pretty intuitive. It is one of the featured applications in the Ubuntu Software Centre.

For creating web graphics, Inkscape (also a featured app) may be a better tool. It creates files in SVG format and can export to the usual .png, .jpg, .bmp etc. SVGs are good because they are scalable, so don't deform when resized. They also have the ability to be interactive using Javascript. SVG is a web standard.

Specifically for the 'programming' side of things you could use ImageMagick. It has a command line interface and also has bindings to many popular languages (including C, C++, perl, python, ruby, java). The ImageMagick program and its various language bindings are available from the software repositories.

To automate simple processes such as resizing, you can use Phatch. It is available from the software repositories.

The only real issue interface wise is GIMP is not PhotoShop. So if you learned where things are in PS then GIMP will be a bit frustrating at first. Of course there are some folks who do there best to make GIMP like PS, like GimpShop (discontinued).

Here is a good rundown of Linux based graphics programs: http://www.linuxlinks.com/article/2008091312364896/Graphics.html

For paint.NET? Definitely Pinta. And if you don't mind installing KDE dependencies be sure to try Krita as well.

Personally I barely use anything other than Inkscape, but that's because I do more creating than modifying.