Applications that take time to start have often a so-called splash screen. In most cases this is used to give the user feedback that something is happening. The useful ones give feedback about what is going on often with a progress bar. On the Internet there is no initialisation nor start up. Hence there is no need for a splash screen at all in my opinion.
In the early days a simple picture was used as an intro to a website, quite often it had below the magic words "Click here to enter". Nowadays quite heavy animations using Flash, are used. They take some time to download, even with a fast connection. Sadly many designers think that every visitor has a high speed connection. Sometimes there is a "skip intro" link. It makes you wonder why there is an "intro" in the first place. Worse, some Flash developers put the skip link inside the animation.
Many animated intro pages use music or sound effects, which might annoy the visitor even more if it's unexpected.
Another good point to consider not using an intro or splash screen is that a web page only containing an animation has no real content and often doesn't show up at a good position in most search engines. So most, if not all, visitors coming via a search engine might never see your intro web page with animation, unless you redirect them to this web page first, which is also a bad idea.
It you really want to show off your Flash capabilities I recommend using separate pages to display them. This way you can make as many as required which might even attract more visitors to your site.