Thanks to everyone for all the advice and suggestions. I would have preferred to have written this some weeks ago; however, I've had some problems: the new hardware had various issues and needed returning to be fixed; the old hardware came out in sympathy and stopped working; and then a week in bed with a virus. All in all, July was not my favourite month this year.

Anyway, everything's more or less back to normal now. Here's what I ended up doing:

• Firstly, after much deliberation, I went with a Cygwin solution to provide the UNIX-like environment I wanted. This is working well.
• Cygwin came with this perl:

  $ /usr/bin/perl -v
  
  This is perl 5, version 26, subversion 3 (v5.26.3) built for x86_64-cy
  +gwin-threads-multi
  (with 7 registered patches, see perl -V for more detail)
  [download]

• I installed Perlbrew using pretty much the default instructions on that page:

  \curl -L https://install.perlbrew.pl | bash
  perlbrew install perl-5.30.0
  perlbrew switch perl-5.30.0
  [download]

  All of this ran without any problems at all. Now I have:

  $ perl -v
  
  This is perl 5, version 30, subversion 0 (v5.30.0) built for cygwin-th
  +read-multi
  [download]

  There were a lot of comments on various forums about how Perl could not be run successfully on Windows without a substantial amount of jumping through hoops. This may be true for earlier versions of Cygwin (I have 3.0.7), Windows, or Perl: I encountered no such problems.
• I then used the cpan utility to install my usual collection of modules. Probably 95% just installed without any problems; there were no insurmountable problems with the rest (which mostly just needed a different dependency install order from what I had been using on the Mac).

So, overall I'm very pleased with this. I have everything I need for both personal and $work Perl coding.

Thanks again to all who helped.