As someone who supports applications running MySQL, PostgreSQL, MongoDB, and Riak currently (ordered by number of servers) I wanted to take a moment to weigh in on this. The bar for entry to a database such as MySQL or PostgreSQL (via EnterpriseDB) is really so low that I wouldn't recommend using SQLite for more than just a preliminary exploration of rails. The abstract nature of your interaction with the database through rails means that you really won't be interacting with the database directly very often. Once you do reach that level of complexity you are you are probably pushing the capabilities of SQLite, and will benefit from having some base interaction knowledge that you have accumulated gradually over time.
Seven Databases in Seven Weeks is also an excellent read for what you are asking, but its handy to have a computer nearby so I wouldn't quite call it a beach read. You'll notice a review in there from Dr. Nic @ Engine Yard that pretty much says it all. This particular book is really good at explaining the use cases that each database engine is good for answering. Some applications are actually well served by having more than one data repository type behind the scenes.
Just a thought for NYC-rb in general: We've hosted several DB talks @WNYRuby and they tend to be really well attended and reviewed. If you haven't already I highly recommend reaching out to DB groups, 10Gen, Basho, etc to see if they'd be interested in sending a speaker to one of your meetups. We recently hosted Dan Crosta (@lazlofruvous) at a DB Seminar through BuffaloLab (not WNYRuby) here; he is from NYC and provided an excellent overview of MongoDB.