I would recommend going with a cloud storage solution instead a dedicated server, because of the reduced maintenance requirements, ability to scale on demand, and lower costs.
I am using Microsoft's Azure cloud for a solution I'm currently building, but Amazon's S3 is an almost identical alternative as a storage service. With small variations, Microsoft's and Amazon's prices are in the range of USD 0.10 - 0.15 per month per GB stored. In case you decide to consider these, you can check the Azure and S3 sites for specific pricing details.
Regarding performance, as I mentioned, my experience is with Mircosoft's Azure cloud and I haven't had any issues with downtimes or bandwidth bottlenecks. I'm pretty sure Amazon's offering is solid, too.
Hope this helps.