Is there any online database or printed reference work where it's possible to look up a character and see it written in many different styles, like different printing fonts, cursives and pictures from classic calligraphy works?
There are in fact a few websites out there, not to mention hundreds of book titles. You may want to try guoxuedashi.com, which has one overview page for each character (eg http://www.guoxuedashi.com/zidian/672C.html) and many sub-pages, one of them indeed with a nice overview of writing styles with pictures from historical sources, such as http://shufa.guoxuedashi.com/672C/.
Actually, we don't have so much different kind of handwriting styles in Chinese. Usually there are two types: regular script (楷体) or running script (行体). Regular script is just the standard writing style and the running one is something we write when we write faster.
Mobile software Pleco has this function, here's a look at the charter 好
So the order is something like:
Seal, cursive, running and regular scripts.
(They're not all free though)