Have you tried a blog site like Wordpress or Blogger? I use both, and they're pretty good.
It's easy to get started, and you don't need to know any technical stuff unless you like want to really customize how it looks.
Also they have kind of like mini social networks within them, so you can meet other bloggers and writers that might be interested in what you write.. That's what I'm counting on anyway!
I usually write a part of a story as one post, and then share that page out to Facebook and stuff. Then when I have a bit more inspiration, I write the next part and keep going like that. It's a good way to stay organized.
Also you can save each post as a draft so you don't need to go live with your chapter until it's fully ready.