I've been writing a fanfic since this summer (currently at 16k+ words), but I'm a very finicky writer, and very slow and unmotivated as well, so I'm waiting until the whole thing has been written and proof-read (and translated) before publishing anything. This way I wont write myself in a corner or feel pressurised to release a new chapter. Since I'm basically pouring my heart and soul in this fic, I want it to be my best storytelling. I'm having fun writing this anyways, so if it takes months, so be it. I'll certainly be happy when it's done though
I have been writing a fanfic on another website years ago in a episodical way, but it didn't have any real weaving or foreseeable ending, and stopped when I got bored. My current SDV fanfic has a clear synopsis and I know exactly where I'm going, so I made the choie of writing it all at once, as a book (it's still chapter based though). It's all up to you to choose your own way, and fanfics are indeed an excellent way of training your creative writing skills. Since you are using preexisting material, it reduces the amount of world-building and really allows you to concentrate on the writing itself.
In any case, good luck