The reason why it wouldn't be good to run all that stuff directly from the cigarette lighter is if the wire guage used for the lighter is too high. You can figure this out by adding the maximum amp load that all those devices carry together and seeing if its less then the tolerances of your cigarette lighter which you can figure out by looking either in the owners manual or possibly written somewhere on the socket itself. You may be safe with all that if you don't run a lot off the inverter, most cigarette lighters shoudl be able to handle a max amp load under 7 amps ok, but its starting to push it then and it might not be wise to continue to use your cigarette lighter to power other devices through the socket, if you can avoid it, you should.
The best way to hook up all your devices is run your own wire (fused of at least 10 guage, 8 if running a long distance or higher amp load) directly from the battery and have it triggered on and off directly by a relay tied to the igition or ACC line. You generally don't want to tap into any other power line thats hooked up to another device used by the car and draw large amounts of current from it as you may take the power needed away from those other devices. The cigarette lighter is your second best choice, but not recommended for a permenant install.