Most free books are typically pdf or epub format. EZPDF Reader handles both. There's no real need to focus on a particular app.
Best thing is to focus on (legal) download sites. If you're into Science Fiction, go to
Baen Books Science Fiction & Fantasy - Home Page. They have a free library with some of their most popular books. Most are essentially first in a series to encourage you to buy more of the series. Just start googling for free ebooks. Some are legit. Just be careful. Some are pirate sites. But there are great places like Gutenberg and others where you can get tons of stuff.
I think I had my ereaders over a year before I bought my first non-technical book.