Dreamhost's standard shared hosting works great for backups due to the huge disk space they give you although you have to stay under the radar since it's not officially permitted for such use.
They will also work with regular pages or low resource scripts as long as you stay under about 1,000 - 3,000 uniques and don't care if the site goes down every now and then or gets throttled and you have backups.
But with the offer Amerinoc put on the table I think you'd be a fool to go with Dreamhost provided the plan suits you. While I have no experience with them I can't recall anyone saying a bad word about them.