As far as I think, you can first upgrade from version 1.5 directly to version 1.9 and then go upgrade to 2.0.
Create a development copy of your store database in its entirety.
Create a dev folder and extract a fresh copy of version 1.9 (no modules or themes from your old 1.5 version, please - just the pure magento 1.9)
Copy over your media folder.
Edit your dev local.xml to point to your new dev db.
Launch the site in your browser and wait for the update script to finish (which could take a very long time)
Either repeat the same procedure for 1.9 to 2.0 upgrade or just use the migration assistant.
If you're still in the consideration stage, keep an open mind about re-platforming your store too. Check out this article for more insight: http://www.matridtech.net/blog/is-it-time-to-upgrade-or-re-platform-your-magento-store/
Better yet, just outsource the operation to an offshore Magento development firm. That too won't cost much.