How are website localizaiton price quotes generally done? I use OmegaT.
Get the HTML pages directly from the client. If the client wants you to download it, do so, and then do a word count in OmegaT. Then send the word count to the client so that he can confirm that those are the pages he wants translated. It is easy to miss something when downloading a site, and you could also download something superfluous, which results in extra work for no extra pay.
Is there a way to come up with some kind of word count from the source text that needs to be translated, which would include, for example, the "alt" texts for links and images, but not the urls, etc.?
My opinion is that unless stated otherwise, you should translate everything that is visible and that will not break the functionality of the site. One exception to this would be the search engine related metatags -- they're not always visible but they should be translated or adapted for the language.
A nice thing about OmegaT's HTML filter is that you can select which elements you want to translate. So in OmegaT, go Tools -> File Filters, click on HTML, and click Options. The alt-text and title-text is included in the translation by default, but you can exclude it. Excluding it will also exclude it from the word count.
To get a word count in OmegaT, simply reload the project, and then go to the file in the folder ProjectName/omegat/project_stats.txt. The statistics also show the file names and their subfolders, if your project's source texts have subfolders.
If the client sent you the web site zipped, you can unzip it to a folder and copy the entire folder to your /source/ folder in OmegaT, even if that folder contains subfolders and non-translatble stuff. When OmegaT creates your target documents, it will recreate the folder structure and copy untranslatable files over.
Ask the client if he wants you to rename the files (and if so, remember to translate the URLs correctly in OmegaT). Since OmegaT uses the same file name for the target file, you'll have to rename the files manually in such a case, at the end of the project.