I've had the SD200 for about a year now, and I love it.
The delay between pressing the button and taking the picture is one second at the most, and really doesnt cause any problems. If you are worried about sports where timing is crutial, you can press and hold the shutter button halfway down which will bring up the focus box (where the camera thinks you want to focus), and wait for you to press it the rest of the way. That press will instantly take the picture.
As far as the LCD screen issue, I think it's more about care/handling your camera. When i bought it i first carried it in my shorts pocket, or cargo pants pocket. One morning I awoke and found the screen cracked and non functional. I bought another one, returned the old one, and started fresh. This time i bought a small, soft, leather case from amazon.com (the case is black and says Canon ELPH on it in gold). It was like $20. Since then, i've had the camera for about 9 months with no problems at all. It still fits nicely in my pocket, and only takes a second to take out of the bag and snap some pictures.
I do like the idea about the neck lanyard thing instaid of the wrist strap.
The only bad thing about the camera is that it doesnt have a battery charge indicator. So i can't tell if it's fully charged, halfway charged, or about to run out. The only thing it does is blink a red battery a minute or two before its about to shut down for good.
Overall, I'd recommend it. Maybe upgrade to the SD300 for more mpixels now that they're cheaper.