What are the different types of indexes, what are the benefits of each?

OdeToCode has a good article covering the basic differences

As it says in the article:

Proper indexes are crucial for good performance in large databases. Sometimes you can make up for a poorly written query with a good index, but it can be hard to make up for poor indexing with even the best queries.

Quite true, too... If you're just starting out with it, I'd focus on clustered and composite indexes, since they'll probably be what you use the most.

Oracle has various combinations of b-tree, bitmap, partitioned and non-partitioned, reverse byte, bitmap join, and domain indexes.

Here's a link to the 11gR1 documentation on the subject: http://download.oracle.com/docs/cd/B28359_01/server.111/b28274/data_acc.htm#PFGRF004