A controller is a component in the ssd. No need to purchase one.
The Crucial C300 ssd's are connected to either a SATA II (3 Gb/s) port or a SATA III (6 Gb/s) port on your motherboard. As long as your motherboard has a SATA II or SATA III port, the the ssd will work. However, performance will not be as good if you connect to a SATA II port.
Although the Crucial C300 and other ssd's are SATA III (6 Gb/s) rated, data will transmission will never reach the full 6 Gb/s. There are a variety of technical reasons for that.
Check you HP owners manual or HP online to find out which type of SATA ports your motherboard has.