I priced this out somewhat recently, and the lowest price I could get renting a server with >=2TB of storage is $11/month using the OVH Eco line, and that's without ECC (which I consider to be non-negotiable), FS-level compression (IIRC you can't change file systems with OVH), or redundancy in case the server/disk fails. I'm currently working on a DIY setup with two nodes equipped with 8GB ECC memory, 2TB of storage (with Btrfs compression to get even more storage out of it), and considerably more processing power than the OVH servers. My total up front cost is going to be about $400, with an estimated $25/year in electricity. The most comparable OVH offering would cost $403 in the first year (with RAID but without a second node), so my DIY solution basically pays for itself after that, and I can upgrade the hardware anytime I want.

Of course, there is an obvious argument to be made that my time is worth more than the cost savings, but I've been learning a lot so I instead consider it a free education. :)