You are going to lose 9V whether you do it from 14 to 5V in one step or in many steps.
The energy you lose (heat, in Watts), is equal to Volts times Amps. V=9, so if, say, you were running something at 1 amp, you would lose 9 Watts. That is a waste of power, and would need a heatsink, and would flatten the battery after a while.
But a picaxe only uses 0.003A. So that is only 0.027W. That is hardly worth worrying about, especially when you bear in mind that the human body, when resting, is using 100W.
So if you just want to run a picaxe (and maybe flash a led intermittently or other low power things), use a low power 5V regulator eg LP2950.
If you are switching something high power, maybe use a BC547 transistor to drive a relay, and make the relay a 12V coil one. Drive the gate of the transistor with a 2k7 resistor - that uses hardly any power. Try to make all the high power things 12V rather than 5V - which is pretty easy in the automotive world anyway. Motors, lightbulbs etc are all 12V.
If you are really stuck and you have a 5V high power device and you cannot do it with 12V, then look at a switching regulator. But even then, I'd buy a pre built module rather than trying to build one from components.
If you can afford a few dollars, maybe look at mosfets. I've used BUK555s in the past and they can switch up to 60 amps and the gate can be driven from 5V directly from a picaxe and they use no power. The picaxe manual contains some fet examples and more modern (cheaper) mosfets. A mosfet would be the simplest way to get a picaxe to turn on (say) a car headlamp or defroster, because it is just one component.
As for power supply spikes, yes they are there. But I've had a circuit controlling my car radiator fan and it has been going 2 years now. It is a LP2950, picaxe, BC547 driving a relay which turns on the fan. I put 470uF 25V across the input to the LP2950, 22uF 6V across the output, and 0.1uF across the picaxe power pins. And it sits in the engine bay just near the battery, and it is in a plastic box. With a retrospectoscope I'd probably put it in a metal box. If you are really keen you could put in some filtering with inductors,resistors and capactitors.