Do you really need this to be at home? I'd look around for a DC and rent some servers there. Benefits:
- no need to worry about the cooling
- no need to worry about the power supplies
- they won't depreciate as quickly
- you can always get rid of them when you don't need them
- you can upgrade them to better servers if you still need the processing power
- expand way beyond what a regular chasis offers if you need
- ah yeah... doesn't take up any space at all at home
Downside is that DC may be not in a close proximity to you, but then again, how often do you stroke the server? If you're processing large amounts of data you may need to transfer it there somewhere. Which leads to another question, can you not get that data directly uploaded to the servers in DC. Alternatively, pick a DC near you and you can go there and do whatever you need to upload the data.
I've got few servers (in a DC) for a personal use, cost me around $70. 2 CPU 4GB RAM 400GB HDD. They're rather old (3 yrs old) but I'm still ok with them. Will upgrade (at $0 cost, just a plan change) when I need to. Let's say you need 10 of those for your application, that'll make it $700/month, or $7k/yr (when getting 10 you most def will get a discount). This is just a starting price for the blade chasis, not including blades and other bells and whistles.
From economical POV it is not efficient to buy any of the computing equipment, unless you're a super large enterprise.