I suspect there might be some variation site to site. Some sites have more people looking for marriage some site have people looking more for hook-ups (and everything in between). First thing to do is determine which type of site you want to be on. Second is to figure out if that is the type of site you are on.

Personally, when I used online dating (mostly match.com), I would be the one to push to meet for coffee quickly. I felt that talking through emails and even the phone made it so much harder to get a sense of who the person was and if it was likely to turn into anything. I didn't want to waste MY time coming up with cute and witty emails for a month or two when they'd meet me and then decide that there was "no spark" (ugh, the most over-used phrase in online dating).

That said, there isn't one right way to do it. People really have different preferences with regard to meeting early or not. You have to do what is comfortable for you.

Lots of luck!
EJ (a married woman, thanks to match.com!)