On GraphicsMy definition of web graphics is often a tongue-in-cheek one: everything that doesn't provide information! And, mostly, that is true. Graphics should be used to judiciously enhance the visual appeal of the site.
It's best when the site graphics combine aesthetics and function, as they often do in navigation buttons. The main rule of thumb here is that they should never detract or distract from the information your visitor has come for.
Probably the most obvious graphic on your page is your logo. And, often it will dictate the color scheme for your site. It's a good idea to visit many sites to look at how others use (or misuse) their logo.
Unless you are designing for 6 year olds, you might want to absolutely stay away from flashing, blinking, animated graphics. At least the ones that go on and on, with no way for the visitor to get them to stop. Unnecessary animated graphics are often the indicator of an unprofessional site.
Having said that, you will often see such graphics on high-end, edgy sites, but on the best ones, they have a time-duration set, or may be used as a "flash page". A flash page is a page that comes up before you actually get into the site, and you need to click on it to get into the site. (I find such pages annoying in the extreme.) They may look absolutely fantastic, but the visitor is there to find information that is supposedly on your site. Thus, that page only serves to delay.
If you want some serious, and thought-provoking information about presenting data and working with charts or graphs, you should definitely get your hands on The Visual Display of Quantitative Information by Edward Tufte. It will really provide an education in how visual information is used and misused. His second book, Envisioning Information may be more directly applicable to web and user interface design and will repay serious study with a tremendous amount of invaluable information.
On a more practical level, is the book I recommend on my opening Advice page: Lynda Winman's designing web graphics.