One of the best and most current sources of appellate information are SCOTUS Blog and SCOTUS Wiki. The blog is great for keeping you up to date - an RSS feed is available or you can use your iGoogle feed application. The wiki links to the original documents filed in the case. The two are joined at the hip: the blog generally links to the wiki page where the documents are maintained.
Here's an example to consider. This last semester one of the LP sections had an assignment that involved an issue about impeachment evidence that was illegally obtained that will (hopefully) be resolved when the USSC hears the case of Kansas v. Ventris. Not only was the progress of the case through the USSC tracked by blog posts, all of the relevant documents were posted on the wiki. The briefs and petition for certiorari are a gold mine of research information.