Personally, I like the "Web page, single file (*.mht)" option. This saves the page and all the graphics in just one file, which can be later decompressed into separate files if you want. But, either option generally works.
Occasionally, you get error messages that the page cannot be saved. I don't know why this happens, but it happens to me all the time on MSNBC. Also, you may want to double-check the file, i.e. double-click it to open it in explorer -- sometimes you only get part of the file, e.g. a header, for some reason. If the web page has an option to "print this page", it is often good to use that and then save (usually you see the same info but it is formatted in a more printer-friendly format).
Sometimes, the "save" and "save as" options are both greyed out. Don't know why, but opening the page in a new window often solves that.
I have Adobe Acrobat on my system, so if worse comes to worst, I choose Acrobat Distiller as my printer, and then print the web page as a pdf file. If you've got Fax software installed on your system or other software that creates special sorts of printers (e.g. Paperport), that will also probably work.