Try KeeperFX - http://www.gog.com/forum/dungeon_keeper_series/keeperfx_hires_dk1_latest_builds_and_install_instructions/page1

The KeeperFX mod in triock's link isn't the current version.
Here's the KeeperFX homepage:
http://keeper.lubiki.pl/html/dk_keeperfx_dwnld.php

And here is the currently most active Dungeon Keeper forum. There you'll get everything you need.
http://keeperklan.com/

Is the version from GOG the same as the one listed on the KeeperFX page?

If I can install the KeeperFX CCP, will that help me to address the graphics resolution problem that I'm having?

As someone who is not that technically savvy with mods, would I be better off using the KeeperFX with installer download?

Thanks very much for your help!!

Dave

I think you should really go through the thread I posted (even though it has an outdated link to KeeperFX, sorry I didn't check it before), it's not that long and it can helpyou to answer your questions. ;)

triock is right, it's all written in the tutorial from devilhood. Yes, you can use the current GOG version with KeeperFX CCP no matter if you use the zipped file (it's zipped with the freeware 7-zip) or the installer from their homepage. The only tricky part with GOG's version is that the in-game music won't work out of the box, because DungeonKeeper plays the Audio from the original CD. This CD is included in GOG's version as an image file, which you can use in a virtual CD drive (see devilhood's instructions). Anyway, all other sounds work, so if you don't need the music tracks you can skip this part.
As for your resolution question, yes, you can set custom resolutions in the file keeperfx.cfg. Just open it with any text editor and change the according entry to your liking. DungeonKeeper supports three different in-game resolutions that can be set and switched while playing by pressing Alt+R (but not in the game's main menu).

INGAME_RES=640x480x32 1024x768x32 1280x800x32

This is great. Thank you!