There are a few possible approaches. To give a specific sentence I will choose this sentence out of "Chasing after the American Dream". which I picked up randomly from Google.
As long as a person measures their own worth by comparing themself with others,
Here the author uses "themself", but possible simple substitutes are the ones you gave:
As long as a person measures his own worth by comparing himself with others,
This would be traditionally correct, but not politically correct.
As long as a person measures his/her own worth by comparing himself/herself with others,
This is traditionally not correct with the slash, but is politically acceptable.
As long as a person measures his or her own worth by comparing himself or herself with others,
Both correct grammatically and politically, but annoyingly wordy, and perhaps cloyingly politically correct.
As long as a person measures her own worth by comparing herself with others,
Here there is a deliberate breach of the traditional protocol of using the masculine as the generic, instead using the feminine as generic. Not correct, but politically laudatory or some, though again, depending on your point of view, rather cloying and distracting.
Often balance is sought by mixing up the gender. Which is fun, but can be even more distracting, leaving the reader with the impression that they are missing some semantic to the capricious gender.
As long as Mary measures her own worth by comparing herself with others,
Here we actually begin changing the sentence itself. By using a concrete person rather than a generic, we can solve the problem, however, obviously it needs to be properly integrated.
As long as a one measures one's own worth by comparing oneself with others,
Here we give a more specific substitution, using "one" instead of the third person. Again this is a change in meaning, but it can be used to convey the same sense (as it does here.)
As long as a person measures self worth by comparison with others,
Here we make a more dramatic structural change to the sentence to eliminate the use of the problem words, which is also a more difficult change, but can lead to the best results.
Finally, in certain circles you can use artificially created gender neutral pronouns, for example, "eir" for his/her, "emself" and for "himself/herself", though there are several alternatives. These are known as Spivak pronouns and are CERTAINLY not standard or appropriate for regular communication, but in certain specific, narrow circles might be considered appropriate:
As long as a person measures eir own worth by comparing emself with others,
I don't much care for this, and it exudes a political agenda, but it is one option you might consider.
See Wikipedia: Gender Neutral Pronouns for more.