I'm looking for a good book or website that has good information on Fae: different types, personalities, looks, abilities, etc. Sort of a Fae dictionary. Any ideas?
Can I assume you've spent some time with google? Don't be insulted if you have. We get many such questions from new members who haven't started with a series of google searches. Don't stop with one. Use other keywords to broaden or narrow your search, as needed.
I have done a bit of Googling. It seems like a lot of the results are more for people who "are" fae or vampires. I've found a few that have decent lists of different types of fae but the descriptions are pretty weak. I'd like to find something a bit more in-depth. I suppose I could just work off of one of the lists and Google the individual types listed, but it would be much easier if I could find one detailed, well-organized list.
Try demonology, list of demons, Babylonian myth, etc. searches on Wiki/Google. Wikipedia is a source with many lists, try it out.
Fae—although being a valid term—has been used in recent years by writers who steer away from the more generic fairy. Celtic and Irish mythology were particularly rich when it came to fairy lore, or anywhere in the United Kingdom when it comes to that. The Seelie and Unseelie Courts, the Tuatha Dé Danann and the Tylwyth Teg are great places to start your research.