As someone once mentioned in a video I was watching, one word processor is hardly different from another. Let's compare it to drawing programs, for instance.
I've seen many an artist hopping from one program to another while working on the same piece, simply because program A might be better for sketching, program B for coloring and C for the finishing touches.
Word processors, however, are basically the same thing. Notice how Microsoft Word's functionality has hardly changed over the years regardless of it having gone through countless iterations since its first release. This is because all you need to write any document is simply basic formatting options, a spell checker and maybe the option to import media into the document.
Notepad, however, lacks those features. I recommend you use any proper word processor just to give your document some proper formatting before releasing it instead of it being just one massive wall of text. I'm not talking about anything too fancy, making titles bigger, bold and centered as well as polishing the text alignment should be far more than enough.
As to which programs to use, well, as I've said, they're more or less the same. LibreOffice and OpenOffice are both completely free office suites which include a word processor, the other alternative is Microsoft Office, but I wouldn't pay for it just to write a fanfic (I wouldn't pay for it in general, as the two I mentioned either are roughly the same thing minus the fancy interface).
Hope this helps.