If you go to the Capitol first, there is an inside...

If you go to the Capitol first, there is an inside walk way to the library that takes 5 min. The library itself is gorgeous! A must see. You don't need a reservation or a tour, you can explore on your own. Definitely wait in line to see the reading room. It's beautiful. There's other exhibits like early maps, Jefferson's library, and the Gutenberg bible.