Hi I have 2 ways of designing my site.
1) With separate pictures for everything
2) one whole picture and make parts of the image clickable.

Which one is faster in load time?

#1. Downloading multiple images is faster than one big image. Also because when you download multiple images at least something is showing on the page - when you download a single image, depending on what type of image and what browser, there may be nothing showing until the whole image has downloaded.

Additionally, if they share the same background colour, you may be able to use that colour in the table, then when you slice the image you can slice into smaller images while using the table background colour to fill in the spaces.

Look at large sites with lots of graphic content - you'll find they invariably slice larger images into smaller ones.

Actually, I'd actually recommend the opposite. Your overall image sizes are going to be smaller if you combine them as much as possible. You can use CSS to position your image backgrounds so you can get the image you need. The method is called a CSS sprite. Of course, it also helps if you use repeating backgrounds, minimize the amount of images on your page, and optimize your images by saving them as a flattened PNG. Elisor does have a good point on what appears first on the page, though.

If you want to learn more about speeding up your webpage, I'd recommend the YSlow plugin for Firefox, this video, this webpage, and a tool called Cuzillion.

For people like me in outback Australia, we get S*** all internet speed, when someone makes a site with a whole image it takes ages to load, if ya split em mate, bob's ya uncle.