Yes, I believe that Serena Williams is the greatest woman tennis player - she may even be the greatest tennis player, regardless of gender! Serena Williams is an incredible athlete: she continues to break records, compete at the highest levels and, also important, win. It is interesting to note that over the arc of her career, she has improved over time.
Selena Williams has an advantage over other tennis players who came before her, like Billy Jean in that she had access to more support and better coaches and other resources, which helps to make her the best female tennis player and quite possibly the best tennis player of all time.
Yes, Serena Williams is the greatest woman tennis player ever. She is actually one of the best tennis players in history, as is her sister Venus. She has proven her skill, love for the game and athleticism by winning multiple titles around the world. She is an amazing athlete, and did for tennis what Tiger Woods did for golf - turned it into an actual sport instead of an elitist activity reserved for the "haves" of society.
The problem with Serena is that there aren't any great rivals for her, her ease with taking a break and then coming back to dominate highlight that the women's game has been very weak. It's also well understood that she would have difficulty in winning any match against anyone man in the top 300. So there's a good argument for her being best sportswoman of all time, but hardly best sportsperson.