Find a place...
Find a place with lots of cameras on display and snap a picture with each to see how long it takes.
I assume you know you can hold the button down half way and it'll focus, then press the rest of the way and it'll snap with no delay at all.
Actually, I think any camera will do, as they all have about a one-second delay, which is plenty fast enough. It'll take at least five seconds to grab your camera, turn it on, and point it, so the extra half second you might get with a "fast" shutter won't really matter.
BTW. The secret to taking a good picture is to take several and throw away the bad ones.