Actually you do not. SATA-III which is about all you are going to find to buy in the market, will downclock and work fine at SATA-II speed on a SATA-II interface, which is what you have on your motherboard. Any 2.5 inch SATA SSD will work fine. That model is a bit difficult to service, however. Let us know if you need any help.
Absolutely positive you can use a SATA III drive on that computer. All the thing you posted is saying is that the motherboard chipset theoretically will support SATA III. My memory is that on that model the ports are actually SATA II but again it makes no difference. You can use a current model SATA III SSD like Samsung 860 Evo 2.5 inch.
Be alert for scammers posting fake support phone numbers and/or email addresses on the community. If you think you have received a fake HP Support message, please report it to us by clicking on "Flag Post".