Really, Specs don’t have to be huge for a backup server. its only used once a night. Don’t go out and order a server with a 1ghz proscor and 1gig of ram, (although, if you had them money and didn’t know were to spend it, why not drop it here

). You wont need anything more then 500mhz +, 128mb-256mb RAM and a HD big enough to back up your current server and maybe a future one.
Their are a few places were you can do this, build your own server to run dedicated, but unluckily for you, I cant remember them

.
I think the best suggestion would be to:
A) Get a server in the same company, so you wont need to pay for bandwidth, as you are just transfer between 2 servers that may be 20 feet away.
B) Build your own server and get it hosted. (you will be paying for alot of bandwidth if you update every night.)
C) Have 1 extra HD added to your ded and have a Cron job update it nightly. That’s probable the cheaper solution, But if your server goes down, you will have down time. With the other suggestions, if you set your DNS right, you will always be up.