Let's clarify a few things.
"Shutter lag" is the term for the delay between when you push the button and when the camera takes the picture. A long shutter lag causes you to miss shots because your subject has moved, quit smiling, or otherwise changed during the gap between when you pushed the button and when the camera started taking the picture. This is an inherent characteristic of the camera. You can't change it without changing cameras.
"Shutter speed" is the term for how long the shutter is open while the camera is taking the picture. In bright sunlight, this is nearly instantaneous. In dimmer light, the shutter stays open for a while. When that happens, not holding the camera perfectly still results in a blurry picture. Also, movement by your subject can make them blurry. More light will give you faster shutter speeds. Some other camera settings (ISO and aperture) will also give you faster shutter speeds.
"FPS" or "Frames Per Second" is the measure of how many pictures your camera can take in a second. If you put your camera in continuous shooting mode and hold down the button, it will start taking pictures. Some cameras can't take more than one picture every couple of seconds while others can take 10 pictures in one second. Some cameras have multiple speeds for FPS, but most don't. Also, most cameras can only take so many pictures in a row before the slow down and have to wait on the memory card. Getting a faster memory card can help a little with this problem.
"Recharge Time" is the term for how long it takes for your flash to be ready after taking a picture. The flash sucks up power from the battery and then releases a bunch of it in an instant. It then takes time to suck up more power. Fresh batteries or Lithium batteries can help with the flash recharge time.
As a general rule, newer cameras suffer less from shutter lag. Also, DSLR's have almost no shutter lag.
