I've just found my very first armor that I'd like to edit from being a retexture into a stand alone craftable suit. Can anyone tell me the best way to do this?

At the moment, there are two ways to do this. First uses only the Construction Kit, the other uses an external programme called NifSkope. I'm not too familiar with the CK way, but I can tell you how to do this via NifSkope.
First of all, thake the texture folder from the mod and place it into your Skyrim ->Data folder. Then, rename it to something unique, so the result should be like Skyrim -> Data -> Textures -> (armor) -> my armor. You do not need to rename the textures themselves. Now, let us assume that you want to make a standalone Elven armor. In your Data folder you will find Skyrim - meshes .bsa file. *.BSA files are a form of compression, so you will have to extract the meshes you will need. For that you will need a programme like .bsa unpacker or some such. At the moment I do not have link handy, but searching TESNexus should yield some results. Once you have the meshes extracted, place them all to a file in your data directory, for example something like this: Skyrim -> Data -> Mesehs-> armor -> armor. Now, the funny part comes. You will have to open every mesh you exported and assign it the new texture you want it to have. That is where NifSkope commes in handy. Open the mesh in it and to the left you will see "Block List" window (if not, you will have to enable it: Wiew -> Block List). There search for "BSShaderTextureSet". Depending on the mesh, there can be several of them. If you clic it you will see details in the "Block Details" window to the bottom (if you do not have the window, enable it as in the first case). The second line here reads: Textures and there is a small violet flower next to it. In front of the word "Texture" there is a small triangle, if you click it shows all the various textures. Right click on each used line (the one that lists a texture path) and choose Texture -> Choose. Then navigate to the new textures (do not forget to keep the order. First is the color map, then normal map and then sepcific maps). When you are done, save. Here you go. Repeat for every mesh in you new folder.

Hope this helps.