Blue Host offers an inexpensive shared hosting service with an extensive set of of features. Their offering goes well beyond the typical shared hosting features, but for a very low price.
Typical shared web hosting offers PHP and Perl or dynamic websites and little else. They go well beyond this offering Python, Ruby, Ruby on Rails, a number of preconfigured web applications like PHP-Nuke, PHP-BB, Wordpress, Coppermine, Joomla, Tikiwiki. They include the "mailman" software allowing you to set up mailing lists. They even offer shopping cart services and the ability to make merchant account arrangements letting a web site make sales collect money through credit cards.
Yes, for a very low cost you can set up an online store that accepts credit cards.