The reason for using "her" more frequently nowadays is to correct an ongoing imbalance: in general, for a long time, "his" has been used, even where a more neutral pronoun ("one") should have been used instead.
Grammatically, however, any of the recipes you suggest would be appropriate: it is only the matter of the particular taste of the author. I would recommend, though, that when using both "he" and "she," that you use one consistently throughout a particular usage. Don't write "she/her" in one sentence, and then "he/his" in the one after. A few paragraphs later won't be a problem, though.
The reason "one" is not nearly as popular is that it is somewhat awkward-sounding; too many "one" and "one's" in the same sentence makes it feel too stiff and impersonal. (It's a bit of a catch-22, I know, but that's the way it is!)
One other option that you did not mention, though, may be the simplest route of all: simply use collective plural pronouns: use "they," "their," and "theirs." It gives you the benefit of including everybody, without having to contort your writing to do so.
(I would also comment that some books go out of their way to be gender-neutral, particularly through the use of "gender-neutral" names: Chris, Sam, Pat, Jean, and so on.)