closed as off topic by user2683, JeffSahol, Mehper C. Palavuzlar, FumbleFingers, tchrist♦ Jun 8 '12 at 18:57
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That depends on the medium.
When you publish something on the web it can be difficult to use typographic quotation marks, as they don't exist in all fonts installed on all computers over the world. Using typewriter quotation marks would be the safe bet, as they are part of the basic ASCII set, so any font (except Wingdings) has them.
Otherwise typographic quotation marks are always better looking.
I have generally been told to just use the " on your keyboard and not worry about it. If it's for print, the desired characters will be inserted at layout. For online, whoever edits or maintains the site will apply any different characters desired.
My experience, as a writer and as editor (or whatever you'd call the person who takes Word docs and publishes them in whatever online form is called for), is that manuscript or copy should be submitted in the plainest fashion possible. Look at submission guidelines and you will usually see a plea for no fancy fonts or typography.
I'm not sure this answers your question. I read it as asking someone writing something to be submitted to someone else for publication.
Definitely use curly quotation marks if you can. If you can't, no one will fault you for using the straight or typewriter quotation marks.