They do go inside of colons and semicolons.
Single quotes are for quotes inside of quotes.
If a quote is three lines or more it should be indented. When you indent, quote marks become unnecessary and you should not use them. You should use quotes only for a specific purpose. Do not use them because you think you should. It is often better to paraphrase and use a footnote to tell the reader the source of your idea or statement rather than quote sentences or words verbatim.