I was typing my post when you posted yours. Sorry I missed it. And really sorry for screwing everything instead (ouch
That interface is SATA.
If you wanna use it as a general use external drive, you can get a case for it that converts it to USB. Just make sure it supports SATA drives. If you just wanna have those files on your new computer, just install the drive as non-system drive to it. It will fit no worries, provided that the case has the space and there is a free SATA power and data cable inside.
The main internal storage interface these days is still SATA, the same of 2005. It just changed internally to provide faster connection, but nothing physically.
Frankly, I feel like I'm mixing things up here. Hopefully I understood what you want originally.