Photography is light. Deciding the best combination of shutter speed and aperture to record that light depends upon your desired effect. The aperture controls the amount of light via the size of the lens opening. The shutter speed is the amount of time that the light is exposed to the sensor. The combination of the two result in the exposure.
When shooting flowers in natural light outdoors, I usually select aperture priority (AV) to control the depth of field, or how much of the flower I want in acceptable sharpness. I can use a large aperture such as f2.8 to isolate the flower from the background. This is often helpful when the background is not integral to the image itself, when the “sense of place” is not an important part of the image. Perhaps the background is cluttered with distracting elements (below, left image). By using this technique, you can isolate your flower and rid your image of that distraction (below, right image).
If it is important to document the whole flower, with sharpness from front to back, I use a smaller aperture, such as f32. This allows me greater depth of field, with more detail in the lotus as well as the leaves and seedpods.
Recording the proper exposure of a white flower needs special attention. Just like shooting in snow, the white flower tricks the camera into trying to make it 18% grey, thus underexposing your whites (below, left image). If the flower compromises a large area of the image, you need to use exposure compensation to override the automatic meter in the camera. In the Av (Aperture-priority) mode, that'll produce a shutter speed one stop slower, brightening the entire scene and delivering flowers closer to a true white tone. Manual exposure users can achieve the same effect, with the freedom to open the lens one stop, slow down the shutter speed one stop, or even increase their ISO one stop (below, right image).
When using flash outdoors, I use aperture priority, not just for controlling the depth of field, but to also control the exposure on the flower. Against a hazy or overcast sky, you have completely separate control of flash illumination on your botanical subjects (via Flash Exposure Compensation) and how sky in the background appears (via standard Exposure Compensation) — with Canon EOS SLRs, the two are always separate and independent. It's easy to raise ambient brightness to lighten cloudy skies, and to deepen clear blue skies by applying some minus compensation.
On occasion, I will use shutter priority (TV) when I want to use the shutter speed to control movement of the flower. Even a very slight wind can affect the sharpness of the flower by tossing the flower in and out of focus (below, left image). As you can see, the flower was in motion using the shutter speed of 1/60. If you wish to stop the movement of the flower, you need to increase the shutter speed. By increasing the ISO from 100 to 400, I was able to shoot at a higher shutter speed of 1/250 while maintaining the aperture of f5.6 that I wanted. When the shutter speed was increased, the flower appears sharp despite the wind gusts (below, right image).
You can use the shutter to create an abstract feel of movement to the flower image. By slowing the shutter speed to ¼ of a second and panning with the flower, you create a flurry of colors, while still recording a sense of the shape and color of the flower (below, left image). The image can be an abstract on its own or used as a backdrop to a layered image piece (below, right image).
Once you decide what is the most important aspect of recording the image, whether it is the movement or the depth of field, you can effectively choose the right shooting mode. If you need to control both the shutter and the aperture at the same time, you could select manual exposure mode. I find manual metering effective when I am using flash as the main light source indoors or trying to mimic a studio shot outdoors with flash as explained in the first article on outdoor lighting.
Choosing the best exposure mode is dependent upon what you are trying to create. Experiment using the various options available to you and decide what works best for your vision.