You should be able to use a 7805 to provide a reasonably clean 5V in an automotive application - as long as some sensible precautions are taken. Back in the good/bad old days, National Semiconductor produced a book called “The Voltage Regulator Handbook” – this was full of useful information regarding using linear regulators in all sorts of applications. I am not sure if they do a web-based version these days, but it’s worth a Google?
Some protection against reverse polarity spikes would certainly be good (due to starter motor spikes and alternator load dumps). This would also protect against a reverse connected battery - but killing your LED/LCD module would be the least of your worries if this happened! Not just reverse polarity voltages are a problem, but reverse current flow through a regulator can also kill it. This can happen if the input voltage is shorted (or falls rapidly) and there is a reasonable amount of capacitance on the output circuit. Protecting against this can easily be done, as mentioned, with a 1N400X diode in the input circuit to the regulator (before the input caps, not between them and the 7805).
Filter caps – as a general rule, 2200uF per amp drawn is a good guide for the electrolytic input capacitor, bypassed with a 0.1uF in ceramic (or mylar) close to the regulator pins. Regards voltage, 25V will probably be enough, but I’d go for 35V in a 12v volt automotive application, if physical size is not an issue. Some application notes mention using small value tantalums close to the pins, although they are high performance caps, I’d be wary of them in circuits that may have voltage surges or spikes - as they are prone to going short-circuit if over-voltaged. Regards the output cap, a similar 0.1uF close to the pins in required, but do not put a large electrolytic on the output circuit, as this can lead to the regulator becoming unstable. If the LED/LCD module requires a certain value cap, then put that on the module supply pins (I’d fit a 0.1uF regardless, nothing is advised).
Does it need a heatsink? As the input voltage is more likely to be around 14V (rather than the nominal 12V of the battery), the regulator would be dropping around 9 volts. So probably not, if the current drawn by the module is under 100mA (although, at 100mA, it would run very hot with a Rthj-amb of 50-60C/W). Large pads and thick tracks around the regulator would help here in keeping the temperature down.