This is one of the reasons I've been building my version of this on top of SQLite: it's incredibly cheap. All you need is a writable disk somewhere. I started with a $5/month VPS.
I'm not actually bothering to run backups because theoretically ALL of the data there can be retrieved from other sources - pulled back out of the Twitter archive exports for example.
But another similar project uses tarsnap for backups, which is pretty inexpensive.
