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Glancing through the threads I get the sense I'd be better off using a controller, but I'd hoped to be able to make due with just the keyboard and mouse.

However, no matter how much I swipe my mouse, maneuver my finger across my laptop's pad, or press down on the number keys for movement, I can't seem to turn my ship at all. Other keys seem to work fine, and I can cruise in a straight line with the 'a' key, but obviously that won't help me much. I'm only as far as the very beginning of the tutorial mission of the first game.

Running this on Win 7. Any help would be very much appreciated.
This question / problem has been solved by crazy_daveimage
Under options room -> control config there should be a setting to turn mouse on/off. I believe it is arrow keys rather than num keys to turn the ship. If you still are having trouble with controls, I would recommend the Freespace Open Engine and playing FS1 through FSport - it makes things more compatible (even with Linux and OS X as well as Win 7) and adds a lot of graphical improvements. The game looks very pretty.
While the arrow keys don't seem to do anything, that on/off setting seems to have done the trick. Feeling like quite the dunce though for not seeing that in options.

Still need to get father into the game before knowing just how well I can handle the controls, but I'll be sure to check out those recommendations if I have any further trouble.

Many thanks!