Hi Azallie and welcome to CDFreaks
Are you just trying to transfer files to the PC or project live image to the screen? The 3 RCAs connectors would only be for the latter, while the usb connections should do both to my knowledge.
If the Sony Vaio VGC-JS200 desktop doesn’t have the necessary RCA inputs, then the usb should be ok, but probably oyu have to install some software driver first - don’t you have a CD accompanying the camera?
Anyways, this should help you out:
Connecting Sony Handycam to Windows Vista Via USB