The best way to deal with shutter lag is to go for an SLR, with them there is no shutter lag and yet there can be a delay.
There are three things that cause shutter lag in most cameras - flash, focus and exposure. Measuring the exposure is the simplest for the camera and usually happens in a tiny fraction of a second. Getting the focus right is trickier, that can take a half second to a second if the subject is easy to focus on, it can take longer if the subject is in poor lighting. On top of that the motor that drives the auto focus mechanism is usually slow and relatively weak to conserve battery power, but that of course delays getting the lens focussed. SLRs have faster more powerful motors but P&S cameras do not. Flash is the third, it takes time to charge up the flash and P&S cameras tend to charge the flash when you press the shutter instead of ahead of time. That's deliberate because this saves power and prevents your batteries from draining even faster.
Dealing with shutter lag is not so easy. Forget exposure, that always happens quickly. Flash can be addressed by keeping your finger on the shutter, holding it down half way until you're ready to shoot. This drains your battery but ensures that the flash is always ready to go. When you're ready shoot you lift your finger briefly and then press the shutter and it should be almost instant ... well ... except for focus.
Dealing with focus is not always easy. If you concentrate on subjects that have clearly defined contrasts the focus can be really fast. But you have no choice about that usually. So like getter the flash ready, you can also point the lens at the subject and hold the shutter down part way to get the focus right. Then press the shutter when the moment is right.
Ok, all that said, there are cameras that minimize the problems. I have a Canon PowerShot G7 for instance. It's a really sophisticated P&S camera though not as sophisticated as my Nikon SLR. The shutter lag on this camera is rarely more than a second, it operates really fast.
One thing that I do like about it however is that it also has a continuous shooting mode. That comes in two flavours. The first is simply continuous shooting, in this case there is a bit of a lag at the start to get the exposure and the focus and after that the camera fires off images at the rate of two or three per second, it's almost as fast as my SLR. However the way it achieves this remarkable feat is to not focus or reset exposure settings after the first shot.
That can be a problem if your subject is moving so there is a second shooting mode called continuous auto-focus. In this case the camera will refocus after each shot. That slows it down a little, I get about one shot per second in that mode but again that's a minimal lag.
That's the best solution I've found to dealing with shutter lag in the P&S cameras. I suppose there are probably a few other models and brands with similar features but I don't know what they are. I'm sorry.
Finally, if you really want to get rid of those problems you have no choice but to go to an SLR. My Nikon SLR rarely ever has any shutter lag. What slows it down briefly is only a rare subject that it can't seem to focus on instantly. It also fires off images at three per second, my other Nikon SLR does that at five per second. The only problem with this solution is that it's very expensive. The camera itself isn't cheap.
If you do want to go this way, I'd suggest a Nikon D40x as an entry model probably with the Nikon 18mm-200mm lens. That is an ideal combination. If you're a sophisticated photographer, the Nikon D80 is better and the D200 is ideal.
I hope this helps a little.