The installer will ask you where you want to install mzscheme, you can choose any directory that is convenient for you. You do not need the option to create links in standard directories, say "no" to that.
Then you'd run mzscheme from the directory that you installed it to.
In what you posted above, you don't include the path to mzscheme. Are you now including the path? If so, what exactly are you typing, and what error message are you getting exactly?
* tried it with the absolute path
* tried it without
* tried running it in its directory
* tried running it without parameters just to see what happens
all of these ways with the exact same output result (except the path changes as it should)
You're going to need to get help on the PLT Scheme user mailing list for this one. (This is the first mailing list listed at the top of http://www.plt-scheme.org/community.html)
Tell them what operating system you're running, including the output of "uname -a", and which distribution of PLT Scheme you downloaded. Mention you need to run PLT Scheme version 372 specifically. No need to include the "-m" or "-f" options or to mention Arc, just show them the output of when you're in the bin directory and you type just "./mzscheme"
Then, once you have mzscheme working, we may be able to help with any Arc problems you have... :-)
Is ./mzscheme a symbolic link pointing to a missing file? Or is ./mzscheme a shell script with an invalid interpreter line? (the first line, beginning with #! )