They can be all independent if you want, but you can use what is called a "Star System" which is basically like somewhat the same characters in different roles in each story, like actors playing different roles. Similar to how Astro Boy's/Tetsuwan Atom's creator Osamu Tezuka did. :3

http://tvtropes.org/pmwiki/pmwiki.p.....haracterDesign

Something like that.

Or they can all exist like parallel universes.

I was considering something like that. In fact, if I really want to, I can just pull a CLAMP and have only two or three stories connected to each other. I kinda don't wanto to overwhelm myself, as I've realized that's why I haven't got started on any other stories yet.