Hi, I'm new here and I apologize if I have posted this in the wrong place. I also want you to know that I did a search but I couldn't find what I was looking for and I did check the FAQs. Please excuse the noobness. Though I have done a lot of PC gaming this is the first time I will be purchasing games frrom the internet such as what GOG supplies. Anyway...
I have moved from a 17" 4.5 screen ratio to a 16.9 in a 24" monitor. I was wondering if I will run into any issues with older games because of this configuration. I actually have a full version of NOX and though it installed and the installation screens were excellent when it came to running it the game screen was jarbled.
Thoughts? Advice? Experiences? Thanks.

What exactly do you mean by jarbled?
If you're concerned about the wider aspect ratio distorting the picture, check the settings on your monitor to see if it has hardware aspect ratio control. I just bought a widescreen myself, and it has a function that automatically letterboxes the display according to the input aspect ratio, so I can play for example a Dosbox game in undistorted 4:3. It seems to work nicely.

Welcome to GOG.
Typically you shouldn't have any problems at all, aside from the fact that some games will appear stretched. This site may be able to help you get the most out of some of the older, more troublesome games.
Also try looking at the override options in your [GPU] control panel. You should be able to set it so that it renders a specific game differently. Using this you could help alleviate your woes.

Check out the Widescreen Gaming Forum wiki for widescreen fixes for most games. In the case of GOG releases you can almost always find such information in the game's forum (often as a sticky). Several GOG releases already have widescreen fixes implemented that are not present in the original versions.
For DOSBox- and ScummVM-based games you don't have to worry about widescreen compatibility because they have full support for widescreen monitors and by default will display the game with its intended aspect ratio rather than stretching it (you can of course override this if you so choose).

Widescreen gaming no problem here. For DOS games just set the correct 4:3 aspect ratio in DOSBox with OpenGL and you will get the best retro-gaming experience you can on Windows machines to date...
Older DirectX games aren't a problem either (on NVIDIA cards at least): you just have to choose from the graphic drivers control panel if you want to stretch graphics or have the correct aspect ratio....