A wind-up is not necessary when you first learn to serve, but it's worth trying, because you'll eventually want one, and some players serve more smoothly and comfortably with a wind-up right away. If the wind-up makes it hard for you to remember other, more important parts of the serve, like bending your elbow or meeting the ball high, it's not worth that cost while you're first learning, and you will eventually find it easy to add later on. To serve without a wind-up, you'll start with your elbow up and racquet down as shown in the sixth photo of this lesson, but don't skip ahead to that photo yet, because you'll need some of the other elements explained between here and there.
Start your toss with the ball just in front of your right leg. Many players start the ball farther forward, but doing so creates a curved toss path that requires releasing the ball with very accurate timing to avoid tossing it too far forward or back. Starting the ball as shown here will allow you to use a straight-line toss path that does not require your toss release to be timed nearly as perfectly. The easiest way to develop a reliable toss is to imagine a straight line from this starting point to the point where you want to hit the ball and slide the ball up along that line.