Pretty much any of them. Though sustained sequential writes aren't all that much different on a spinning disk than an SSD anyway... at least nothing like the huge increase you see on seek based reading and writing (like random access patterns or reading from multiple files).
Are you really sure it's your hard drive that can't keep up? If you are not compressing the video at all 1920x1080x3x60 = 355MiB a second, which means you'd fill a 500GB SSD in 23 minutes. Then sure i can see a spinning disk not doing that unless you have a decent clear RAID setup.
If you are compressing it in some way then the drive probably only has to write at the very most a tenth of that, or about 35MB/s, which on sequential writes almost any drive can do.
For instance, if you are using a video compression that records your video at 50Mbps that means you are essentially writing 6MiB/s to your drive. If your drive can't do that you have some serious problems with your drive. Yet compressing 355MiB/s down to 6MiB/s is no easy task. Which is why I asked if you are sure it's your drives.
What are you using for your recording, and what settings are you using?