(Mount Olympus, from Wikimedia Commons)
As you've probably figured out, nothing is isolated- and that was especially the case in Ancient Greece.
Philosophy, literature, culture, ideals, law, geography, and art all influenced one another to create what we now think of as Ancient Greece.
What does that mean for our research?
These sites are:
When you begin searching, the idea is to get a general idea of the background of and issues surrounding your topic.
It's perfectly fine to start with Google. That's what I do, and I know that many of your professors do the same thing. Reading the Wikipedia article on your site will also help give you a background on your topic, and a sense of where to go next. (Remember that information you find on Wikipedia will have to be corroborated by other sources before you should include it in your paper.)
You probably know how to use google and wikipedia. Here are some more good sources for background information:
Literature Criticism Online (Especially the Topic Finder)
While doing your preliminary research, keep a running list of questions you have and keywords to explore.
Many of the broader questions you have are already laid out by your assignment:
While actively reading your background sources, be conscious about any more questions that come to mind. Having specific questions will help you direct and focus your searches
When reading web resources, or reference sources, you may find people, places, events, ideas that seem related to your site. Write these down as they may come in handy as keywords later!