The correct way to make text italic is to ignore the problem until you get to the CSS, then style according to presentational semantics. The first two options you provided could be right depending on the circumstances. The last two are wrong.
Don't worry about presentation when writing the markup. Don't think in terms of italics. Think in terms of semantics. If it requires stress emphasis, then it's an em
. If it's tangential to the main content, then it's an aside
. Maybe it'll be bold, maybe it'll be italic, maybe it'll be fluorescent green. It doesn't matter when you're writing markup.
When you do get to the CSS, you might already have a semantic element that makes sense to put italics for all its occurrences in your site. em
is a good example. But maybe you want all aside > ul > li
on your site in italics. You have to separate thinking about the markup from thinking about the presentation.
As mentioned by DisgruntledGoat, i
is semantic in HTML5. The semantics seem kind of narrow to me, though. Use will probably be rare.
The semantics of em
have changed in HTML5 to stress emphasis. strong
can be used to show importance as well. strong
can be italic rather than bold if that's how you want to style it. Don't let the browser's stylesheet limit you. You can even use a reset stylesheet to help you stop thinking within the defaults. (Though there are some caveats.)
class="italic"
is bad. Don't use it. It is not semantic and is not flexible at all. Presentation still has semantics, just a different kind from markup.
class="footnote"
is emulating markup semantics and is incorrect as well. Your CSS for the footnote should not be completely unique to your footnote. Your site will look too messy if every part is styled differently. You should have some visual patterns scattered through your pages that you can turn into CSS classes. If your style for your footnotes and your blockquotes are very similar, then you should put the similarities into one class rather than repeat yourself over and over again. You might consider adopting the practices of OOCSS (links below).
Separation of concerns and semantics are big in HTML5. People often don't realize that the markup isn't the only place where semantics is important. There is content semantics (HTML), but there is also presentational semantics (CSS) and behavioral semantics (JavaScript) as well. They all have their own separate semantics that are important to pay attention to for maintainability and staying DRY.