I agree that databases seem boring. I'd been using them for about 10 years before last year when I had to write significant parts of one. Once I started getting under the hood I realized how interesting a lot of the database problems are. Turns out, the geek factor is pretty high. Problems like query optimization, fast multi-dimensional indexing, full text search and so on give a nice playground for CS mojo. :-)
Per SQLite: It is probably the simplest SQL database to learn. However, I fear it might give a skewed perspective on SQL to someone just starting with it. While it's fine for the simplest of applications, if you start building up complex queries, its performance is orders of magnitude worse than almost every other SQL DB, potentially leading one to falsely believe that such things were to be avoided.
I personally find MySQL to be user-friendly enough for starting off with. Though, honestly SQL in general is one of those things that I'm glad to know, but find painfully inelegant.