In Programming class, we were taught that <> = <STDIN>.

That's wrong. <> is shorthand for <ARGV>.

I could write this without asking for user input...the only problem was that one of the args would be a string that may contain spaces, and I'm not sure how best to handle that. Make the user enter that argument with quotes?

Quotes, or backslashes should work in all shells that I know off. (The spaces are special to the shell, Perl has nothing to do with that).