Generally, you should avoid inline styles as much as possible and rely on your stylesheet to apply style settings. Use an 'id' attribute to allow settings that are unique to a particular instance of your <blockquote> element, and 'class' for those that will be shared by several different instances. But by handling everything in your stylesheet, if nothing else, it has the advantage of keeping all of your settings in one place even when the changes affect several different pages. When you have some inline styles and some in the stylesheet, it's easy to make mistakes.
Perhaps there is a more appropriate element I should be using than a blockquote.
What I want to achieve is a "box" for the purpose of making a block of text stand out from the surrounding body text. The box would have a border and a background that is a different color than the background on the rest of the page.
So, is a blockquote appropriate or should I be using something else?