My story is posted chapter by chapter, and I don't know of any way that I could have waited to post it until it was done. It seemed to me that the characters in my story demanded to be read by more than just me. Now I know that I've made mistakes in the chapters, and for that, I'm truly sorry. I'm working on that.
As for reading a story, I usually look for stories that have several chapters already posted. I don't know why, but I always believe that if there are more than a few chapters already posted, the author will most likey continue the story to its end. I'm not always right on that, but it works out most of the time.
I do lose interest in a story with major gaps in time between posts, though. I think the reason for that is that during the interval, I get wrapped up in a completely different story and forget about the one I was reading before. That's bad, I know, but sometimes there's just not enough in the story to make it memorable enough to me to go back every day to look for more.
I'm reading one now that has me really excited, and I check the site daily to find out if another chapter has been posted. This story has me so hooked that I doubt I'd ever walk away from it.
As for mine, I pretty much know what's going to happen in the story anyway, so doing it chapter by chapter isn't so bad. Most of the stuff in the story is drawn from personal experiences and the experiences of friends and loved ones, so it isn't like I'm running off the rails with it.