Do I need registered ECC (RDIMM) or unbuffered ECC for a dual-socket Xeon E5-2670 setup?

You need registered ECC (RDIMM). Unbuffered ECC only works in a single-CPU setup; dual-socket LGA2011 boards require registered DIMMs because unbuffered sticks overload the memory bus with two CPUs. Just hunt down cheap 16GB or 32GB RDIMM sticks for your dual E5-2670 server.