[The Fifth Horseman]

Then it says on the screen, "Z:\c
Illegal command: c."

What am I missing here?

You're missng :
As in, C: is the correct command. C on its own is not recognized as one.

C:\DOSBox-0.72\dosbox.exe* c:\game\game.exe* -conf c:\game\dosbox.conf* -noconsole -exit

That's not how I'd recommend doing it. This way is quite inflexible, may be confusing and is bound to cause problems soomer or later.

This is how I did it with Covert Action:
"C:\Program Files\DOSBox-0.70\dosbox.exe" -conf "C:\Program Files\DOSBox-0.70\dosbox.conf" -conf "C:\Program Files\DOSBox-0.70\Configs\Covert Action.conf" -noconsole
Notice that there are two config files declared. The first one is the default DOSBox config, the second one only needs to contain the options that you want changed from the values in the default config. The -noconsole parameter disables the status console window.
Covert Action.conf is not stored in the main DOSBox directory, but in a subdirectory named Configs. That's because having several dozen such configs in there was a bit confusing (it's easier to manage them when they're all in the same place and there are no other files there).
When you have declared two config files, their autoexecs are both executed, in the order the files were declared.
This is my autoexec from Dosbox.conf:
mount c f:\dosgames\
C:

This is my autoexec from Covert Action.conf
cd covert
covert.exe
exit

Notice it doesn't contain the lines responsible for mounting the games directory and changing to the C drive. It doesn't need them, since they are already executed in the default config. The exit at the end of the autoexec means that when DOSBox gets to that line (when you exit the game), it will automatically close.