Opinions, please: your suggestion for a Slack-friendly desktop environment that is not a challenge for puzzle-lovers. TIA, everybody!

Why don't you save yourself from having to read suggestions for things that you've already decided you didn't like.

What did you try and what did you not like about them?

I do not have a list of desktop environments I refuse to consider. Ease of setup is most important to me.

If you want ease of set-up I would go with XFCE. If your system is sufficiently powerful(good amount of RAM, fast CPU) then you could try KDE. KDE is also straight forward to set-up. I'm a big fan of XFCE.

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KDE, Xfce and MATE (from MateSlackBuilds.org) fit my standards for being easy to "configure" (a word that's at least as open to interpretation as "easy"). Lots of themes, icons, window borders, etc on kde-look.org, gnome-look.org and xfce-look.org. As far as I know, all three have graphical ways of installing these customizations, so you don't need to work with text editors or the command-line. LXDE probably falls into this category too.

My favorite is Fluxbox. No complicated GUI stuff--just simple text files.

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I agree that Fluxbox is indeed nice, but, if the OP wants to add new programs he'll need to edit text files in the Fluxbox menu. The OP is after ease of use hence my recommendation of two easy to use desktop environments that ship with Slackware.

MATE With Compiz is my current favorite. But all the above are good choices.

Please define the word "setup."

Xfce hands down requires the least amount of after-installation configuration.

Minimal effort will require a full Slackware installation. Using the command "xwmconfig" will allow you to choose between all the desktop GUI options. Personally, I am partial to either Xfce or KDE. Lately I have been running KDE on my new laptop since it can handle the extra system resource usage. I run Xfce on my old laptop because KDE gets a bit sluggish on it when Akonadi/Nepomuk start indexing the file system.

I think that KDE is a far more integrated experience than Xfce. Xfce will require you to change very little. KDE will require you to change very little. MATE might be fun, but you have to build that from source in order to use it on Slackware. So it does require some work to get it up and running. In general though, MATE will require you to change very little once you have built it and its up and running. KDE/Xfce are already built on Slackware installations.

There are a number of other options available on Slackware besides Xfce and KDE. There is also Blackbox, Fluxbox, Window Maker, FVWM2, and TWM. I suggest you try them all and see which you like best.

We have binary packages ready at several mirror sites:
http://slackware.org.uk/msb

When I decided to try a DE, I went with KDE as installed by Slackware. It was fine, required no configuration whatsoever, but DE's aren't my cup of tea so I retreated back to fvwm a few months later. Just my two cents.

My sincere thanks to all who passed along their preferences. That has been helpful.

Xfce is very good. Also willysr's Cinnamon works so nice on my system.
I hope one day PV integrate it to the Slackware installer as a middleweight desktop among lightweight Xfce and heavyweight KDE . Cinnamon is not based on Gnome anymore and doesn't need systemd as well.