Thanks for your interest in BackupBuddy!
Yes, you can backup to your local server. You also have the option to send your backups to multiple offsite destinations just in case the unthinkable happens to your server. We now offer Stash to our BackupBuddy customers at no extra cost! You'll have 256mb of free storage, and the option to upgrade if you'd like more.
Depending on how you store your backups you'll have several options on how to manage your backups. You can schedule your backups in intervals of month, twice monthly, weekly, daily, or hourly.
Please let me know if you have any other questions!