I can see a few solutions that I'd recommend. I wasn't sure if your $250 budget number includes disks or not, but if it does, that makes it hard. I also don't know how you are currently serving them - from a server or just your desktop.
1) Manual + cheapest. Buy a set of HDDs and set a calendar reminder every week to copy all your contents over. Swap one to the bank and one offsite. If windows, you can use robocopy or something similar, if Linux, rsync
2) Manual + cheapest + automated. Plug in a drive and use Crashplan to automate the backups. I don't recommend swapping the crashplan store though since you may end up missing content. Leave it plugged in. Crashplan is free to backup to a local media.
3) All NAS setups will cost you more than $250 unless you have all the parts left over from a previous computer. Well, there may be exceptions, there was a deal at Microcenter for a MB+CPU for $100, then you'd need RAM and disk still.
For disks, since these are backups, you could get by with desktop-grade disks. You can get 3TB drives for about $100 bare and an external disk reader for $30 or so. If you wanted to, you could do 4TB white label drives for about $145 as well.
The problem is easier when you're taking about what will fit on one disk. If you have more than 1 disk work of content, then you have to figure out how to break it up or span multiple disks together to get the capacity you need. That's when you really need NAS solutions or something else. Also NAS would give you automated backups so you don't forget vs going the cheap route and setting a calendar event.