It might be useful to give a bit more info on what you need apart from the disk space.
What kind of budget do you have available?
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Your budget is more than enough for a server of this kind. We have built a few servers like this for our selves and usage of backups of our VPS nodes and suggest a setup like this:
i3-3220 or similar processor (you dont need much CPU power)
8 x 3TB WD Red drives in Raid-5
A server setup like that will give you about 20TB of usable space. I would just go with software raid as well if this is just a backup server. Adding hardware raid isn't really going to benefit you at all and will just add another piece of hardware to fail. I think with most providers you should be able to pick up a server like this for around $300 probably.