So I'm running Ubuntu, like the great big Linux newb that I am, and I'm trying to set up my ATI 9600 Pro with dual monitors. I have two very different monitors of very different sizes; a 19" and a 15" CRT. As such, I want to run different resolutions on each of them so that their displays remain relatively the same in terms of size, and I want app windows to only maximise to their current monitor.

I managed to get an extended desktop set up using the same resolution on both monitors, but even then, apps open right in the middle, and maximise across both monitors, which is of course incredibly annoying.

Try this tutorial for a start. It sounds to me like you haven't got Xinerama enabled which helps apps to know which screen they are on and maximise properly.
I'm developing some Java things at the moment and that doesn't honour the Xinerama extension (it maximises at startup and holds onto the window size values, which is annoying). I described my current setup here which maximises everything properly but doesn't let you move windows from one desktop to another (The mouse does though).

As a PS: I once set up a dual head between 2 cards of different types and with different monitors. I tried watching a film in very-widescreen but half was in black-and-white! I guess the colour depths didn't match.

I think this article will be helpful.

http://navetz.com/v/132/Simple-dual-...n-Ubuntu-Linux

It shows you how to dual screen using xrandr. It involves modifying one line in xorg.conf and writing a script. It also works very well with compiz.