Should they be italicized? I have found a variety of responses to this question, what do serious style manuals say? Thanks.
Yes. (Oh, I'll mention this is according to MLA style, but pretty sure it's just general English grammar to italicize newspaper titles)
MLA style has to do with citations, which isn't really relevant to use in the body of a work. However, the answer to the original question is yes. The title of the periodical does get italicized, but only the words that are actually part of the official title. Where this gets sticky is when there is an initial "The". If "The" is really part of the title, such as The Watchtower, it does get italicized. However, it is not part of the title of the New York Times or the Chicago Tribune, so in these cases it is neither capitalized nor italicized. Reference: The Chicago Manual of Style, 15th Edition, 8.180 - 8.182.
It's a style guide that includes more than just citations, like many style guides. Since the OP was looking for specific style guides, I mentioned which my information came from, despite the fact I also mentioned it's pretty much just common English grammar to italicize newspaper titles. Thanks for the personal shout out, though, .