Okay, so I have tried to make some new items using Vanilla textures. This issue seems to primarily happen to (or at least I've encountered it with) clothes and armor. So far every time I'd make a new one, using vanilla meshes/textures, when I go to test it out in the game it tells me that the mesh/texture or both can't be found and causes my game to crash.

I am using a disc version of Morrowind, but I had to unpack the bsa's because I don't have the disc for the construction set. I am also using Windows 8, if that has any baring whatsoever.

So far I haven't had any issues when making new items using other textures/meshes, just the vanilla ones... So any idea as to what could be causing this? And how I can go about fixing it?

You should always include the warnings you see when troubleshooting a problem, so we know exactly what went wrong.

But I'll make a guess...
Armor/clothing uses Body Parts, so you need to make sure those body meshes exist too. Otherwise, all you made were the ground meshes of the armor/clothing. Ground meshes are what the armor looks like on on the ground/shelf/etc. Body Parts are what they look like when you wear them. Two different meshes that need to be assigned for any armor.

Or the opposite happend, and you only made Body Parts and no ground meshes.
I have to just guess here, since I haven't seen your warnings yet