Hmm, that's a hard one.
Some of it depends on what site I'm reading on. For many forum sites, I start by looking for an interesting or catchy title. Some sites also give a blurb with the title. For example, Fanfiction.net has authors give you a little blurb on their story. For those that have this option, I don't usually care as much about the title. Rather, I look at the blurb and I immediately know if I'll spend time on this story because-if it's well written- it tells me their tone, point of view, plot, and everything else that needs to be there to get me interested.
Once I begin reading a story, the first chapter is a huge deal for me. If it's super fast-paced or can't suspend my disbelief (more stories than you would think have Ash catching Dragonite or Arceus in the first chapter).
Lately, I've been a bit more mellow concerning the first chapter and have found a lot of gems that give me something to enjoy my evenings with.
I'm not super strict on grammar, but if there's enough that I'm noticing them all the time I'll usually drop the story.
Summary: Title or blurb needs to catch my attention. The first chapter needs to capitalize on my interest by being well-written and interesting to keep me flipping (er, clicking?) pages.
I hope this answered the question.