So as you can see with this model, for some reason I cannot determine, there are ragged lines in the texture instead of appearing smooth. How would I go about fixing this?
Make sure the UV is correctly unwrapped. If some UVs are overlapping, you will get all sorts of artifacts. Here’s a quick tutorial:
And here’s how to mark seams to correctly unwrap:
Also the texture should be seamless to avoid manual retouches.
How did you “model” your model? I believe N-Gon, duplicated vertices or “non-flat” faces caused the problem (my English isn’t good).