You ought to be able to do it with just about any linux distribution. Pick the one you like the best or are most comfortable with. Then ... scheduling backups to tape ... sounds like you need software, and you've indicated you want something free. Given the tape drive you have, I'm assuming you have other computers to back up?
My personal choice would be Amanda
It is an outstanding backup scheduler and works with native utilities and formats without having to install a bunch of other stuff to get it running. I like it at least in part because it takes care of managing everything with little or no intervention on my part, and it recovers gracefully from a lot of error situations. Just as an example, today I forgot it was running late and decided to shuffle some tapes in the library. I ejected the tape right out from under Amanda. It noted the error, rounded up and catalogued all the pieces of the backups, and sent me an email summarizing the results and advising me that it would finish flushing the backups to tape when a tape was available. Gotta love it.