Why don't you just use the mouse?
If you hold RMB moving mouse you will rotate your ship around (pitch+yaw, unless you select Elite control method in space which gives you pitch+roll, but it's slower, unwieldy and generally sucks).
Pressing LMB while RMB is held fires your laser, when RMB isn't held, you can move your cursor around, select targets and press buttons with LMB.
It's very simple and natural.
The only keys you need to know are enter (fire main engine if in "engines off" mode, increase set speed if in "manual" mode), and shift (fire retro thrusters if in "engines off" mode, decrease set speed if in "manual" mode).
The rest of the keys are displayed on their respective menu buttons and can be bypassed by using your mouse.
Also, use "engines off" mode for combat, it doesn't really turn your engines off, merely disables computer assist giving you full control over your ship, which you will need when being shot at.