If I want to mention the word "furlong", for example, should I use furlong, "furlong", or 'furlong'? Also, am I correct in putting the punctuation outside the quotes?
Any of those options will work, but if you refer to words more than once you should take care to use the same convention in each place. Italics seem the best option if you can use styled text, but styles aren't always available.
It's conventional to place punctuation marks inside quotes instead of outside. There are a lot of situations where that practice leads to ambiguity, though, such as when instructing the reader to type something:
It's good to know the accepted convention and follow it when you possible, but convention should take a back seat to clarity. A typographic convention, such as using italics instead of quotes, can solve the problem by eliminating the quotes, but even then it's not always easy to tell if a punctuation mark like a period is italicized or not: