Infopop does webhosting - however they don't offer CPanel to my knowledge.
The hosting company Jeremy and I own does!
We have lots of threads users who can probably give you a recommendation - including Allen, Nikos, DonJulio, dman, oceanwest and more. We probably host 30+ UBB.Threads sites for ThreadsDev users.
Our plans are located here:
http://www.vertexhost.com/shared.html We keep 3 backup sets - on a second drive. A daily, weekly and monthly.
And for some of my threads consulting clients I keep a MySQL database backup (nightly) on a remote server in a different data center just for added measure.