“Secure” is not a meaningful criterion. All major distributions have similar levels of security: safe defaults and timely security updates. Just stay away from obscure derivatives that might vanish or might not keep up with the updates (or from embedded distributions that aren't always good with security but you aren't in that domain space anyway).
To keep your PC safe from harm:
- Don't run commands that you found on some random website and that you don't understand.
- Install your distribution's security updates regularly. (“Beginner-friendly” distributions have a “software center” or similar software where you can click a button to do it, and may be set up to download updates automatically and prompt you to apply them.)
- Stick to the software provided by your distribution as much as possible. Don't install the newest version of a program unless you actually need it. Distributions apply security fixes to the version they ship.
- Run Windows programs in a virtual machine in preference to Wine. If you use Wine, don't allow it to access all your files, only a dedicated directory.
“Has network capabilities” is also not a meaningful criterion. All distributions include all the networking tools you'll need, they're very basic and it would be hard to exclude them from a system.
“Can run Wine well” isn't a very meaningful criterion, except insofar as you'll probably want to have a reasonably recent version, so pick a distribution that updates relatively often.
“Beginner friendly” is a highly subjective criterion. This being said, some distributions are more beginner-friendly than others. Pick Ubuntu, elementary OS or Linux Mint in preference to Debian or Arch Linux.