Whats a good point and shoot digi camera with fast shutter?

you can consider Canon PowerShot SD1400IS 14.1 MP Digital Camera with 4x Wide Angle Optical Image Stabilized Zoom and 2.7-Inch LCD

http://www.amazon.com/gp/search/ref=sr_nr_scat_330...

Nikon Coolpix S8000 14.2 MP Digital Camera with 10x Optical Vibration Reduction (VR) Zoom and 3.0-Inch LCD

http://www.amazon.com/gp/search/ref=sr_nr_i_0?rh=i...

Panasonic Lumix DMC-ZS7 12.1 MP Digital Camera with 12x Optical Image Stabilized Zoom and 3.0-Inch LCD

http://www.amazon.com/gp/product/B00395WIXA?ie=UTF...

Canon PowerShot SX210IS 14.1 MP Digital Camera with 14x Wide Angle Optical Image Stabilized Zoom and 3.0-Inch LCD

http://www.amazon.com/s/ref=nb_sb_noss?url=search-...

There are some things in your questions that tell me you don't understand.

The speed of the shutter has nothing to do with how long it takes for the camera to focus and expose. That is called lag time. All automatic cameras have it. Some say they're faster but the difference can be measured in mili-seconds - that's not very much.

Get used to it, lag time is here to stay as long as you use an automatic camera.

Shutter speed on the other hand is the time it takes to properly expose your photo. If you set the

shutter speed, on an SLR lets say, at 1/500, that shutter will be open 1/500th of a second.

However the lag time to focus and expose may be 2-3 seconds.

There is no getting around lag time. The alternative is manual control with an SLR and that can take many times longer.

All point-and-shoot digital cameras have fast shutter speeds and automatically adjusts to lighting. All of them also have shutter lag.

You are trying to take a shot in dim light. Even dSLRs will complain about that. The difference is with dSLRs, you are allowed to adjust other settings to get a proper exposure. With point-and-shoots, you'll just have to deal with the automatic settings.

Clear bright photos will depend on you, the photographer. If you give the camera enough light, it will respond favorably to you.

I would suggestion these good cameras :

Canon PowerShot SX210IS : 14.1MP, 14x Wide Angle Optical Image Stabilized Zoom, 3.0-Inch LCD, HD shooting capability at 720p with stereo sound, DIGIC 4 Image Processor with evolved Face Detection Technology, Face Detection Self-timer

http://www.amazon.com/gp/product/B0035FZJM6?ie=UTF...

Panasonic Lumix DMC-ZS7 : 12.1 MP, 12x Optical Image Stabilized Zoom, 3.0-Inch LCD, Built-in GPS function lets you keep track of your photos by location

http://www.amazon.com/gp/product/B003960FFM?ie=UTF...

Nikon Coolpix S8000 : 14.2MP, 10x wide-angle optical zoom, 3.0-inch VGA (921k-dot) Clear Color Display, 720p HD movie recording, Creative Slider creates pictures, 4-way VR Image Stabilization System

http://www.amazon.com/gp/product/B0034XIM82?ie=UTF...

Sony Cyber-shot DSC-H55 : 14.1MP, 10x optical zoom Sony G-Lens, 3.0-inch LCD screen, HD Movie mode (720p), Capture breathtaking images in Sweep Panorama Mode

http://www.amazon.com/gp/product/B0033VKKB2?ie=UTF...