Disclaimer: I am relatively new to GNU/Linux, and I have installed Slackware 11 onto my computer.

My computer functions perfectly as a desktop, sound, video, mouse, browsing the web etc is all in working order, but I have often read that with Slackware you are in charge of your entire setup.

What is the checklist that a new Slackware user should use to complete their new system? I want to secure it and have all the basic desktop utilities in full function. What does a novice user need to do to ensure that they are not running around with an unsecured and less than fully functional desktop?

First, set up a firewall, I recommend with this:
http://www.slackware.com/%7Ealien/efg/

Have a look in /extra, on CD2 or DVD, see if there's anything you need, such as Slackpkg or Checkinstall.

Read Slackbook. Learn to use iptables, for example create a script for it rather than just use some "easy rule creator" to get the most of it. Check once in a while the released security patches (slackware.org). If everything you need works all right, then don't fix a working thing - applies more or less to anything except security (if you think it works, it doesn't mean it works).

If you're in need of work, consider LFS. Should give you something to do for a while.

If I'm behind a router how necessary is setting up a "soft" firewall?

hardware firewalls are typically quite lame ... try some firewall tests to see:
http://www.hackerwatch.org/probe/
http://www.pcflank.com/scanner1.htm

Hi,

Simple answer, 'Read'!

Check out 'Slackware LQ Suggestions!'. Loads of links with useful information on setup, general use and other guides.