GTK is GTK+, and both GTK+ and QT run on all the distributions you mentioned.

Which you pick probably depends on what programming language you like. C? GTK+. C++? QT. Python? GTK+.

In any case, do some research into how GTK+ and QT work, and figure out which is better for your requirements.

Note on QT: you can either pick the GPL or the commercial license, and you cannot switch! If you want to write a proprietary app AND don't want to pay for QT, GTK+ is the toolkit for you.

XUL (XML User interface Language) is the language the Mozilla products are coded in (Firefox, Thunderbird, Sunbird, etc.). The code is XML, JavaScript, CSS, and SVG, so web coding skills are applicable. The resulting application will run almost identically on any platform for which there is a Xulrunner application (Linux, Win32, Mac, Solaris, ...), and often run perfectly the first time on an untested platform. Java and Flash applets can be included inside XUL programs as well. On many platforms, Xulrunner does in fact use GTK underneath, but it is hidden to the application programmer. It is possible to build a very powerful application in few lines of code, by reusing Mozilla objects.

A XUL application will generally perform better than a Java applet and will consume fewer resources.

The downside is that XUL is not well documented, especially on how to get started. For advanced projects, it is necessary to study code from Firefox, etc. to figure out how to do something.