Welcome to the Apple discussions.
I have a 1.67Ghz Powerbook with 2GB ram running Leopard, and it runs fine. I would recommend it, as it's the last operating system upgrade available for OS X. Depending on your software, you may have to upgrade some, as I did, however, there were no additional charges for any upgrades to run under Leopard.
Call 1-800-MY-APPLE and ask if they have 10.5 Leopard available. It's not available in the stores anymore, and if the Apple store is still selling it, it's the least cost new version available.
Whether it's 10.5 or 10.5.6, you'll want to install the combo 10.5.8 update, which provides all updates through 10.5.8, regardless of what you've started with. Repair permissions, then install the combo update, then repair permisssions again. Then run Software Update several times to pick up other updates. The combo update is available from
http://support.apple.com/kb/DL866