Checking out a book.

This function generally falls under the umbrella of Integrated Library Systems http://en.wikipedia.org/wiki/Integrated_library_system

You might investigate some of the following

http://drupal.org/project/millennium
http://drupal.org/project/sopac
http://drupal.org/project/xc

There's been other threads in this group on the subject http://groups.drupal.org/node/40772

http://drupal.org/project/merci was designed for equipment lending, but can be used to manage the reservations and checking/out of anything. MERCI handles late fee calculation and grouping books into "buckets" of like books for reservations/wait listing. This helps streamline the workflow so users aren't waiting for copy #5 of Grapes of Wrath while copies #1 and #2 sit on a shelf.

MERCI is more focused on letting users make their own reservations and controlling which groups can reserve which content types for what duration. It would take a fair amount of UI and View work to get MERCI to work well for a small library, but because MERCI doesn't leverage another catalog system, it has a lot of the features you are looking for. Everything from printing your own barcoded labels (http://drupal.org/project/merci_barcode_labels) to managing concurrent and monthly/weekly quotas (http://drupal.org/project/merci_quota).

If you only have a few hundred items you are lending, MERCI would work. Once you get into thousands of items, you should probably be looking at the modules @c4rl recommended.

Koha
http://www.koha.org/

Evergreen
http://open-ils.org/