To get the greatest throughput, your going to want something hooked to the bus. I would recommend an add-in RAID card for SATA drives, similar to this model which boasts 10 SATA connectors:
Don't RAID the drives together, just have individual volumes.
I've have no experience with that brand, but that single card could get you where you need to be for $800. General speaking, add-in RAID cards work great for this type of work. I would do a quick cruise on ebay to see if you can grab any used SATA-III RAID cards, and put them in multiple PCIE slots. 12x drives in an enclosure off of a single eSATA connector is definitely going to cause some bottlenecks.
Also, as pointed out in the comments, this card pictured could cause a performance bottleneck due to 10 cards sharing one PCIE slot. Your best option would be to go with 2 4-port cards, and if your motherboard can support it, plug the rest of the drives in directly.
I would count how many drive headers your motherboard has, add one for your OS drive, then subtract that from your total of 12 and buy the appropriately sized RAID board. Make sure you buy the correct type for your drives, SATA or SAS. SATA has individual connectors, SAS has one long connector.