Moving from a BlackBerry to an Android, there is no "direct" backup file type that will accomplish this. I've used Verizon's Backup Assistant to transfer contacts from a BB Bold to an Android OS phone without any issues.
Text messages are something else. If you are using Verizon's Integrated messaging app, you can back up your texts and then restore them on the new device. There may be other third party texting apps that allow backups as well.