There are several ways to ensure you can use your preferred fonts on the Web.
First of all, you can use images with headers without hurting SEO. The text is either shoved offscreen or covered with a graphic.
There are also some more complicated (to my mind) text replacement methods using Flash and other techniques.
Most current browsers support @fontface (a CSS method) but you have to upload multiple font versions for the different browsers. The font files can be big (bad for downloading) and when I’ve tested @fontface on pages, the text looked funny. There may also be a problem with font licensing; your desired font might be restricted from being stored on a server.
For body text, here’s a list of fonts you can expect computer users to have.
If you’re not building the pages yourself, just tell your Web production person what you want and let them take care of it.