The maximum data transfer rate of a SATA 2 port is 3Gb/s (300MB/s). The maximum data transfer rate of a SATA 3 port is 6Gb/s (600MB/s)
I don’t know the models of the HDDs you’re looking to buy, but I would be surprised if they had a data transfer rate higher than 136MB/s.
Hard drives may be SATA 3 "compatible", but they are not SATA 3 "capable".
In essense you are quite right in that you would need a decent SSD to take advantage of the SATA 3 capability of your board.