Fraps for recording.
The best ship for screenshots or videos is the sidewinder. People look out of the top of the cockpit which has an unobstructed view. If making videos they likely remap the joystick so that the directions of movement are easier to figure out when looking out of the top of the canopy.
You can also use the 4x multiplier on High-res screenshots (Alt+F10 in Solo/Private Group modes). This gives you a lot more leeway when it comes to cropping the images as you could potentially lose 3/4 of the content and still have what you actually wanted in frame at your actual resolution.