EXAMPLE : A small sign at the business reads: "JIMMY FRANCO'S PRIVATE INVESTIGATIONS".
To me, it makes sense to formulate it like the above.
I agree, however you can stretch the quotation marks outside as well, e.g.
A small sign at the business reads: "JIMMY FRANCO'S PRIVATE INVESTIGATORS."
As far as I'm aware it's down to personal choice. I'd go with your way.
The rule for american style guides is punctuation always goes inside quotation marks. There isn't a separate rule for after colons, probably because colons are also a proper way to convey dialogue, like when she said: "Commas and periods always go inside quotation marks."
I think british style is either the opposite, or at least allows for terminating punctuation outside quotation marks under certain circumstances (Seb's response makes me feel it's the latter.) And I tend to slip into this mode from time to time as a matter of personal taste, especially when the quotations are not setting off dialogue per se, but something like what you've got in your example.
The main thing to keep in mind is just to be consistent. Chances are, whichever way you do it, it's going to have to change to match whichever style guide the publisher looking at it uses. And that's why publishers pay proofreaders and line editors.
Unless you know which one they use, in which case you could emulate that, whether it feels right or not. To be on the safe side, follow Strunk and White, or Chicago Manual of Style. They're the ones most prevalent in america. And by safe I mean that if you already folow their style, then it's less work for them to make your work publishable, so more likely to make it out of the slush pile.
I believe the only exception to putting punctuation outside of question marks is if you are asking a question and the quoted material is not.
Example: Who said "ask not what your country can do for you, but ask what you can do for your country"?
However, apparently (just learned this), if you ended that with an exclamation mark, the correct way would be "... for your country!" and you'd just drop the question mark.
In case you're wondering, if you're quoting a question, you don't double the question marks.
I don't like the rules on these things.
In this example with the sign—or any text-based visual you're describing (newspaper headlines, etc)—small caps would be appropriate for its lettering without quotation marks. Small caps are capital letters rendered at the reduced height of lowercase letters, still drawing the necessary attention but less jarring.
With a screenplay you wouldn't use quotation marks at all, just write it in capitals.
