BeautifulSoup is a great way to go for HTML scraping. My previous job had me doing a lot of scraping and I wish I knew about BeautifulSoup when I started. It's like the DOM with a lot more useful options and is a lot more pythonic. If you want to try Ruby they ported BeautifulSoup calling it RubyfulSoup but it hasn't been updated in a while.
Other useful tools are HTMLParser or sgmllib.SGMLParser which are part of the standard Python library. These work by calling methods every time you enter/exit a tag and encounter html text. They're like Expat if you're familiar with that. These libraries are especially useful if you are going to parse very large files and creating a DOM tree would be long and expensive.
Regular expressions aren't very necessary. BeautifulSoup handles regular expressions so if you need their power you can utilize it there. I say go with BeautifulSoup unless you need speed and a smaller memory footprint. If you find a better HTML parser on Python, let me know.