Welcome to SPCR.
On the Z87 vs Z97, i would go with Z97 mostly becuase there were some issues with Z87, more in line with USB3 that were later resolved with a new version, but also some Z87 boards have high latency, while seems the Z97 has been tweaked better and has lower overall latency.
For the most efficient.... hard to say, i personally have had very good results with Intel, but out of getting out of the motherboard buisness, i would recommend to go with AsRock. Why are you looking into Z97 with 4960T? look into H97 board, maybe something like ASRock H97M-ITX/ac LGA 1150 Intel H97 HDMI SATA 6Gb/s USB 3.0 Mini ITX Intel Motherboard
, it should be the same for your use, also go with the standard 4690 none T, unless you do need the low profile cooler.
As a last recommendation, check Vicotnik HDPLEX H1-S and ASRock mini-ITX
, he uses mainly mini itx asrock motherboards and has some very nice low power setups.