Hi John,
Eclipse is good enough for Android development. Thanks to a special plugin, it has a decent integration with all the tools necessary for development for this framework. Alternatively, you can use any editor which you like (say, Vim or Emacs) coupled with Ant build system if you find it convenient for you. There's no such a strict restriction like XCode for Apple. You may use any tool which suits you best, it's up to you.
Speaking about first project, I'd recommend an application which gives you search results from, say google, youtube, twitter whatever simultaneously. App should handle first X pages from search result and keep information in an SQL table (keywords, title, search engine name). User shall be able to cancel search and the table shall be cleared with second and following search queries. Clicking on the result shall open a browser (or other suitable component, for example YouTube player) with respective link. Last query shall be kept in application settings and automatically be shown when the app is launched again. You might want to add geolocation features and anything else what you fantasy will suggest as well.
Going through implementation of these features you'll get acquainted with common concepts like multi-threading, basic things like ListView and ListActivity, their adapters, using SearchDialog, SQLite, dealing with app preferences and many others useful things.
As of documentation, Android dev site is pretty good as a reference guide not as a learning tool. If you want to learn basics (and advanced technics as well) in Android, I'd strongly recommend books from this guy -
http://commonsware.com/. For $40 you'll get 3 books with free updates through a year. That guy really knows its stuff. Otherwise there's a plenty of free sources of information from StackOverflow to occasional blogs on the Internet, though not all of them do things right.
Happy Androiding! :)