Best if they're not too heavy in Kbytes. Dimensions depend on your website design and the effect which you want to achieve. Best if they are with 72dpi quality (for example images used for printing better be @300dpi, but then they require more Kbytes and load much slower). Colours - all that you have in case of photos, if your question is about design-specific files (such as backgrounds, buttons, etc.) then it gets a bit tricky - best to use (if possible) "web-safe" colours. As for the format - it depends what's on the image - if a photo, then jpg, if solid colour or transparency requred - gif or png...
Images and color combination plays very important role in web designing. Images should unique and light enough to load fast and have a proper alt text for all. Color combination should be pleasing and according to niche. I have found a great article about colors of website on internet and think that you will find it helpful: http://sixrevisions.com/web_design/colors-in-web-design-an-exploration/